Unsteady Effects on NO_x Measurements in Pulse Detonation Combustion

Abstract

Emission measurements from unsteady combustion systems such as Pulse Detonation Combustion (PDC) are challenging due to the inherently large variations in pressure, temperature, composition, and flow velocity of the exhaust gas. Comparison of experimental data is additionally complicated by differences in operating conditions and gas sampling setup between different facilities. Qualitative considerations with regard to the sampling process from PDC, based on one-dimensional simulations, indicate a systematic influence of the sampling setup and extraction process on the resulting concentration measurements. Therefore, operating frequency, sample time, fill time, as well as PDC outlet and probe geometry were varied experimentally in order to assess the degree to which each of these parameters impact the resulting measured ${\rm NO}_{\rm x}$ in order to better inform researchers of these effects when making measurements. It was shown that measured ${\rm NO}_{\rm x}$ emissions can vary significantly depending on the choice of these parameters and therefore care must be exercised in order to reduce the influence of the sampling technique when aiming for comparable results.

1 Introduction

Combustion systems are required to become increasingly more efficient, while at the same time allowing for compact and easily maintained designs suitable for a more decentralized energy infrastructure. Because pressure gain combustion (PGC) systems can potentially provide significant advances in all of these aspects, research interest towards fundamental research and practical applications remains strong.

One of the earliest concepts in PGC, pulse detonation combustion (PDC) was first introduced by Zel’dovich (2006) and is still investigated today as an alternative combustion method for aeronautic (Kailasanath 2000, 2003) and power generation purposes (Kailasanath 2009; Roy et al. 2004; Giuliani et al. 2010). Its main feature is the consumption of a premixed fuel-oxidizer mixture by a supersonic detonation wave traveling through the combustion chamber. This requires a cyclic operation with periods of purging and refilling, as depicted in Fig. 1. The combustion chamber primarily consists of a tube that is filled with a combustible mixture of fuel and oxidizer (2). Conventional combustion by means of a spark plug is initiated (3). This is followed by a rapid deflagration to detonation transition (DDT), which is usually enhanced by constricting the tube’s inner diameter or supporting shock focusing by geometry alterations. The developed detonation wave propagates (typically at a velocity of several thousand meters per second) (4), until it reaches the tube exit (5). Here, the leading shock wave is reflected as a rarefaction wave that initiates the blow-down or exhaust stage of the cycle. During this phase, the combusted gases are expanded and further accelerated towards the tube exit (6). As soon as the inner pressure has fallen back to the initial pressure (or even below due to an overexpansion of the combusted gases and a subsequent back flow), the cycle can be re-initiated (7). The range of pressure differences between each phase is significant. For stoichiometric ${\rm H}_{{2}}$–air detonations starting from atmospheric conditions as encountered in this work, peak pressure of the shock wave is about ${28}\,\hbox {bar}$ but quickly decreases to an equilibrium pressure after combustion ($p_2$) of roughly ${16}\,\hbox {bar}$. The final pressure of the combustion products ($p_3$) before the arrival of the first expansion wave from the tube exit depends on the upstream boundary conditions but typically ranges in between ${5}\,\hbox {bar}$ and ${10}\,\hbox {bar}$.

Fig. 1

Schematic depiction of a pulse detonation cycle

More recent work was focused on the interaction of the PDC’s outlet conditions with an attached turbine (Rouser et al. 2014), as well as the potential of detonation based rocket engines (Wang et al. 2015) and turbofan engines (Xisto et al. 2018). Other studies have targeted increased operating frequency and thermal power output (Frolov 2014), characterization of the acoustic signature of the PDC (Anand et al. 2018), and the facilitation of the detonation initiation process by means of shock waves (Driscoll et al. 2016).

However, in addition to its potentially significant increase in thermal efficiency through constrained heat release (Heiser and Pratt 2002), the harsh conditions behind the detonation wave in terms of pressure and temperature also give rise to concerns with regard to pollutant formation, especially ${\rm NO}_{\rm x}$. Earlier numerical studies by the authors Djordjevic et al. (2017), Hanraths et al. (2018) indicate the potential for very high ${\rm NO}_{\rm x}$ emissions from PDC, which could introduce serious concerns for practical applications of this technology but could be mitigated by appropriate dilution methods. These findings were confirmed by Xisto et al. when simulating a PDC based turbofan engine (Xisto et al. 2018). Yungster et al. (2004, 2006), and Yungster and Breisacher (2005) investigated ${\rm NO}_{\rm x}$ emissions from PDC operated with hydrogen or Jet-A fuel for varying equivalence ratios and fuel charge lengths. Numerical simulations found high ${\rm NO}_{\rm x}$ emissions for near-stoichiometric conditions which also showed a strong dependence on residence time. Altering the equivalence ratio to leaner or richer conditions significantly reduced ${\rm NO}_{\rm x}$ values. Residence time dependence was also found to decrease for off-stoichiometric mixtures. Experimental validation was sought for equivalence ratios of $\phi =0.8$ and $\phi =1$ for PDC operating frequencies of $f={28}\,\hbox {Hz}$ and $f={37}\,\hbox {Hz}$. Although overall trends agree reasonably well, a direct comparison is made difficult by the cycle-averaged nature of the experimental results. Schauer et al. (2009) measured NO and CO emissions downstream of a PDC operated with an ${\rm H}_{{2}}$–air or ethylene-air mixture at $f={10}\,\hbox {Hz}$ and found them to be comparable to the numerical results from Yungster et al. (2004) and Yungster et al. (2006) in both scale and depicted trends. Frolov et al. (2011) also measured ${\rm NO}_{\rm x}$ concentrations inside a methane-air fueled PDC with results below those of conventional combustion systems, which he attributed to the reduced combustion time and the rapid expansion during the exhaust stage in the PDC cycle.

Overall, direct comparison of experimental and numerical data on ${\rm NO}_{\rm x}$ emissions from PDC in the literature is complicated by large differences in operating frequency, charge length, purge ratio and purge gas composition, and sampling positioning.

An additional challenge is posed by the fact that common technologies, regulations, and “best practices” for the extraction of exhaust gases for emission measurements have been developed primarily in the context of steady combustion systems and thus are difficult to apply to transient systems (Rasheed et al. 2011). This does not only apply to PDC but also to all other forms of unsteady combustion systems such as the pulse jet engine (Paxson and Kaemming 2014; Lisanti and Roberts 2016) or the shockless explosion combustion (Yücel et al. 2020), where recent approaches in emission measurements revealed a large scatter (Qatomah et al. 2018). A recent review study of pollutant emissions in various pressure gain combustors also comes to the conclusion that—due to the inherently unsteady nature of these devices—measurement biases are prevalent and a better understanding of these influences is necessary (Anand and Gutmark 2019).

The goal of this study is therefore a systematic investigation into the technical challenges and implications of gas sampling for emission measurements from the unsteady, cyclic combustion system in the PDC. The impact of several key parameters on developing a systematic sampling technique will be investigated. Considering the significant variation in experimental apparatus, operating cycle design, emissions analyzers, and sampling access, a single “best practice” recommendation is unfeasible. However, this work will endeavor to demonstrate the impact of these common sampling characteristics and thereby better equip researchers to reduce these systematic uncertainty and increase the comparability of their measurements.

2 Experimental Setup

This section provides information about the experimental facilities of this study and allows for an overview of the operation conditions and investigated parameters.

2.1 PDC Test Rig and Gas Analyzer Capabilities

The current design of the PDC test rig is derived from the one that was developed and tested previously in Gray (2017), with the latest changes in design described in Völzke et al. (2019). The combustion chamber has an inner tube diameter of ${30}\,\hbox {mm}$ and consists of an injection section (shown in detail in Fig. 2b), a deflagration to detonation transition (DDT) section, and a measurement section (Fig. 2a). Within the injection section, a fixed air mass flow of ${36.1}\,\hbox {g/s}$ is mixed stoichiometrically with hydrogen supplied by three automotive injector solenoid valves. Mixing is enhanced by a jet in cross flow configuration of the fuel lines. Fill time was ${35}\,\hbox {ms}$ unless otherwise noted, which guarantees that the combined length of the DDT section (${630}\,\hbox {mm}$) and measurement section (${820}\,\hbox {mm}$) is completely filled with combustible mixture. A spark plug is used to ignite the combustible mixture. Reliable DDT is achieved by the insertion of six orifice plates between the point of ignition and the beginning of the measurement section. Each orifice has a blockage ratio of 0.43 while the distance between orifices was ${85}\,\hbox {mm}$. Several ports along the measurement section are equipped with piezoelectric pressure transducers and ionization probes to measure the propagation velocity of the detonation front by time-of-flight. After the exhaust of the combustion products sufficiently reduces the pressure inside the tube, the air flow re-establishes and acts as purge gas.

Fig. 2

PDC test rig

To allow for emissions measurements, the exhaust of the test rig is equipped with a support tube holding the sampling probe. Three different probe designs were used. The layout of the baseline water-cooled sampling probe is depicted in Fig. 3. It has a cylindrical shape with an outer diameter of ${10}\,\hbox {mm}$ and extends across the entire diameter of the tube. The inner sample tube containing the sample gas has an inner diameter of ${4}\,\hbox {mm}$ and a ${1}\,\hbox {mm}$ sampling orifice. The inlet can be traversed across the tube diameter. The sample orifice can be aligned either in the flow direction or at a variable angle to it. The second probe design consists of a thin, pitot shaped tube with a sharpened tip to allow for gas sampling with a minimum of flow disturbance. The third design is flush mounted in the combustion chamber wall, perpendicular to the flow. All probes have the same orifice size and are equipped with water circulation channels to maintain a constant wall temperature.

Fig. 3

Cross-sectional view of sampling system (not to scale) with illustrations of the variation in the combustor tube outlet geometry through the inclusion of various short or long inserts

Figure 4 shows the gas analyzer setup that is connected to the sampling probe through a ${0.5}\,\hbox {m}$ heated sample line at ${190}\,^{\circ }\hbox {C}$. This allows for ${\rm NO}_{\rm x}$measurements on a wet basis within the subsequent chemiluminescence detector (KNESTEL CLD dual BASIC). The wet sample line is also equipped with a nondispersive infrared sensor (NDIR) capable of measuring ${\rm {CO}}_{2}$ and water content to account for chemiluminescent quenching inside the CLD reaction chamber. Pressure and temperature of the gas are measured between the probe and the heated sample line by a piezoresistive pressure sensor and a Type-K thermocouple, respectively. Additional pressure and temperature sensors are located at the inlet of the CLD. The CLD was calibrated to measurement ranges of 0 to ${500}\,\hbox {ppm}$ and 0 to ${2500}\,\hbox {ppm}$ using calibration gases of 500 and 1000 NO in N₂, respectively.

Fig. 4

Emission measurement analyzer setup

In parallel to the wet sample line, a dried gas sample is used for measuring the oxygen, hydrogen, and ${\rm {CO}}_{2}$ content by means of a paramagnetic sensor (ABB Magnos 106), a thermal conductivity sensor (ABB Caldos 27), and an NDIR sensor (ABB Uras 14), respectively. Both the wet and dry sample lines are each equipped with a gas vacuum pump drawing in sample gas at a constant volumetric flow rate of ${7.2}\,\hbox {l/h}$ and ${60}\,\hbox {l/h}$, respectively.

It is important to point out that, even for comparably low operating frequencies, none of the measurement equipment in the gas analysis section of the test rig is able to accurately capture the small time scales involved in one cycle of a PDC. The CLD displays a response time of less than a second. In combination with the time delay introduced by the length of the sample line and the measurement train, which is of the same magnitude, the maximum recognizable frequency of the emission system is of the order of ${1}\,\hbox {Hz}$. Hence, all information acquired through these analyzers is averaged over the course of many cycles.

All analyzers require a constant supply of sample gas. As a consequence, if sampling times are to be varied during PDC operation, a solenoid switching valve is placed downstream of the sampling probe to select the source of the sampled gas from either the combustion chamber or a diluent in the form of a mixture of 25% ${\rm {CO}}_{2}$ in Ar.

2.2 Remarks on Gas Concentration Measurements in an Unsteady Flow Field

This section addresses the systemic challenges that are posed by emission measurements in a pulsed combustion environment. Eventually, the purpose of all emission measurements is to quantify the amount of pollutant particles (or pollutant mass) that a specific combustion process releases into the environment. In most cases, an analysis of the total amount of exhaust gases is neither feasible nor necessary. Instead, continuous emissions monitor (CEM) systems usually extract small gas samples under controlled conditions, with the actual measurement producing the pollutant concentration within this sample volume. To still allow for conclusions with regards to the total amount of emitted pollutants, it must be ensured that the composition of the sample is representative of the composition of the total flow. For systems that show a steady-state behavior, both in terms of combustion and their flow field, this usually does not pose a problem, provided that exhaust gases are sufficiently spatially homogeneous at the sampling position and that sample composition is not influenced by the flow field in the vicinity of the sampling probe.

However, experimental assessment of pollutant emissions from PDC requires extracting gas samples from a highly transient flow with cyclic combustion events. This creates several challenges for the traditional concept of emission sampling: The first issue arises from the fact that all flow properties are now varying with time during each combustion cycle. The lack of a steady-state value leaves two choices to adequately quantify the emission of measured pollutants from the system: Either measurements must be able to provide time-resolved species concentration data, or a sensible reference value that incorporates all temporal variations must be defined. The former is usually not feasible since most CEM systems exhibit a considerable delay in the range of several seconds due to their measurement principle, large internal volumes in the sample train, or the method of gas sampling. Thus, when using these systems in the context of cyclic combustion such as PDC, the resulting concentration measurements will only represent a quasi-steady-state average result. This leads to the second issue, which is whether the obtained average concentration is a faithful representation of the total pollutant emission per cycle and thus the desired sensible reference value. As will be shown, this primarily depends on how well the supply of sample gas to the sampling system is able to capture the temporal variations of the exhaust gases.

A faithful representation of the amount of ${\rm NO}_{\rm x}$ from a combustion system would allow one to deduce the total amount of emitted pollutants $n_{{{\rm NO}_{\rm x}}}$ in relation to the overall mole output of the system n during a defined amount of time, thus it should be possible to derive the total mole fraction

$$\begin{aligned} X_{{\rm NO}_{ {\rm x}}}^{{\rm tot}}=\frac{n_{{\rm NO}_{\rm x}}}{n}. \end{aligned}$$

For transient systems, the total amount of moles must be regarded as the time integral of the corresponding fluctuating molar flow rates so that

$$\begin{aligned} X_{{\rm NO}_{ {\rm x}}}^{{\rm tot}}(t)=\frac{\int _{t_0}^{t} {\dot{n}}_{{\rm NO}_{\rm x}}(\tau )\,d{ \tau }}{\int _{t_0}^{t}{\dot{n}}(\tau )\,d\tau } = \frac{\int _{t_0}^{t} X_{{\rm NO}_{\rm x}}(\tau )\,{\dot{n}}(\tau )\,d{ \tau }}{\int _{t_0}^{t}{\dot{n}}(\tau )\,d\tau }. \end{aligned}$$

(1)

However, with both the total mole fraction $X_{{\rm NO}_{\rm x}}$ and ${\dot{n}}$ being functions of time, the resulting $X_{{\rm NO}_{ {\rm x}}}^{{\rm tot}}$ depends on the chosen integration period.

To illustrate this, Fig. 5 uses results from a one-dimensional simulation of a detonation wave, as already employed for similar conditions in Hanraths et al. (2018). Here, the detonation itself is regarded as a planar, one-dimensional phenomenon in accordance with the ZND model¹ that can be represented within the frame of the reactive Euler equations, that is, as an inviscid and nonconductive but chemically reacting compressible fluid. To this end, the simulations apply an HLLE approximate Riemann solver in parallel to the multi-step chemistry of the ${\rm H}_{{2}}$–${\rm O}_{{2}}$ kinetic mechanism by Burke et al. (2012), which has been extended by the San Diego ${\rm NO}_{\rm x}$ submechanism (Hewson and Bollig 1996). The numerical domain represents a simplified combustion chamber with a continuous air supply as depicted in Fig. 5a, where the gas sampling process is emulated by tracking the flow properties close to the chamber outlet. Before ignition, the chamber is completely filled with a combustible ${\rm H}_{{2}}$–air mixture. A precalculated ZND profile is used to initiate the detonation at the left boundary of the domain. After propagating through the tube and exiting towards the environment (detonation phase), the open end boundary condition causes an expansion wave that reduces the post-combustion pressure until it falls below the supply pressure of the continuous air supply (expansion phase). The ensuing purge phase replaces the remaining combustion products inside the combustion chamber with air (purge phase).

Fig. 5

Influence of unsteadiness on gas sampling from PDC exhaust stream

The graphs of Fig. 5b–e depict the temporal evolution of flow properties such as mass flow ${\dot{m}}$, ${\rm NO}_{\rm x}$ mole fraction $X_{{\rm NO}_{\rm x}}$, pressure p, and gas velocity u at the sampling position during a full PDC cycle. Since the following discussion is aimed at a qualitative analysis of their time dependent behavior, scales are omitted. The initial detonation induces a strong peak in the mass flow ${\dot{m}}$ that is followed by expansion waves that cause the flow to exit from the combustion chamber. Eventually, a constant air mass flow reestablishes during the purge phase. The distinct phases are indicated by colored areas. Even though the detonation phase displays the steepest gradients, due to its short duration most of the ${\rm NO}_{\rm x}$ molecules are encountered during the expansion phase until the point that the concentration drops sharply when purging ensues.

Due to the high temperatures and the sufficient availability of ${\rm O}_{{2}}$ for near-stoichiometric detonations, NO formation is dominated by the thermal path. In this case, a coarse estimate of the kinetic time scale of ${\rm NO}$ formation is given in Heywood (1988) by

$$\begin{aligned} \tau _{{\rm NO}}=\frac{{8 \times 10^{{-16}}}T\exp \left( {\frac{58300}{T}}\right) }{\sqrt{p/101325}}. \end{aligned}$$

(2)

While peak values of temperature and pressure within a stoichiometric ${\rm H}_{{2}}$–air detonation wave can reduce this to $\tau _{{\rm NO}}\approx {7}\,\hbox {ms}$, these conditions only last for far less than ${1}\,\hbox {ms}$. Therefore, combustion product conditions after the main heat release has already occurred and during the subsequent expansions waves are the defining ones to estimate $\tau _{{\rm NO}}$, which results in values of the order of $\tau _{{\rm NO}}\approx {150}\,\hbox {ms}$. Comparing this to the typical particle velocities of the combustion products that range between 100 and ${1000}\,\hbox {m/s}$, resulting in residence times on the order of ${30}\,\hbox {ms}$, it becomes clear that, even though thermal NO forms relatively fast during the short and intense detonation phase, residence time within the combustion chamber is insufficient to reach equilibrium conditions except for very long tubes.

With the combustion chamber assumed to be fully filled with combustible mixture and its length fixed, the chosen cycle duration ${\varDelta } T$ (that is, the period of the PDC operating frequency f) defines the length of the purging phase.

As a result, the integral value of $X_{{\rm NO}_{ {\rm x}}}^{{\rm tot}}$ is primarily influenced by the length of the purge phase and continuously declines for increasing cycle length ${\varDelta } T$. It is worth pointing out that due to the strong variations in mass flow, the value of $X_{{\rm NO}_{ {\rm x}}}^{{\rm tot}}$ calculated using Eq. 1 is distinctively different from a simple time averaged mole fraction defined by

$$\begin{aligned} \overline{X_{{\rm NO}_{\rm x}}}(t)=\frac{\int _{t_0}^{t}X_{{\rm NO}_{\rm x}}(\tau )\,d\tau }{\int _{t_0}^{t}\,d\tau }. \end{aligned}$$

(3)

As can also be seen in Fig. 5d, correcting the absolute pollutant concentrations to a fixed exhaust oxygen content of 15 vol% allows for elimination of the effect of increased air dilution during longer purge phases, as the corrected value remains constant. This effectively results in a total concentration value $X_{{\rm {NO}_{\rm x}}}^{{{\rm ref}, 15}}$ that is independent of operating frequency as long as the sampling window captures all combustion products and lasts into the purge phase. Similarly, limiting the sampling of exhaust gas to a certain sampling time window defined by ${\varDelta } t$ can have a strong influence on the measured reference concentration, because phases of high pollutant concentration are omitted in the investigated gas sample.

Additionally, all of the above considerations and equations account for the entirety of the bulk flow of the exhaust gases, even though a practical gas sample would extract only a small sample mass flow ${\dot{m}}'\ll {\dot{m}}$, as illustrated in Fig. 5a. Consequently, Eq. (1) would change to

$$\begin{aligned} X_{{\rm NO}_{ {\rm x}}}^{{\rm tot}}(t)=\frac{\int _{t_0}^{t} {\dot{n}}'_{{\rm NO}_{\rm x}}(\tau )\,d{ \tau }}{\int _{t_0}^{t}{\dot{n}}'(\tau )\,d\tau } = \frac{\int _{t_0}^{t} X_{{\rm NO}_{\rm x}}(\tau )\,{\dot{n}}'(\tau )\,d{ \tau }}{\int _{t_0}^{t}{\dot{n}}'(\tau )\,d\tau }, \end{aligned}$$

(4)

when assuming that the sampling process itself has no direct chemical impact on the composition of the gas sample (e. g. by wall reactions or pressure drops within the sample line), species composition of both flows remains identical (i. e. $X'_i(t)=X_i(t)$ for all t). Equation (4) becomes equivalent to Eq. (1) only when

$$\begin{aligned} \frac{{\dot{n}}'}{{\dot{n}}}=\frac{{\dot{m}}'}{{\dot{m}}}={\rm const.} \end{aligned}$$

However, in a practical implementation, it is reasonable to expect that ${\dot{m}}'$ is significantly influenced by the interaction of the flow field at the sampling position with the actual geometrical properties of the sampling probe and the specifics of the sampling train. An impression of the amount of variations in static pressure and velocity can be found in Fig. 5c. For the simplified assumption of a one-dimensional detonation with subsequent purging phase, the interaction of the contact surface with reflected shock and expansion waves creates a complex series of rapid changes in velocity. Even though purging in a real detonation chamber would most likely display a smoother development, rapid changes in the flow field are still to be expected and have been recorded in experiments as well. A simple model could assume the strength of the sample mass flow to be governed by the total pressure at the sample location, i. e.

$$\begin{aligned} {\dot{m}}'(t)\propto p_{\rm tot}(t). \end{aligned}$$

Figure 5e includes the comparison of the temporal development of $X_{{\rm NO}_{ {\rm x}}}^{{\rm tot}}$ as defined by Eq. 1 and an assumed ${\tilde{X}}_{{\rm NO}_{\rm x}}^{\rm tot}$ where ${\dot{m}}'$ scales linearly with pressure so that

$$\begin{aligned} {\tilde{X}}_{{\rm NO}_{\rm x}}^{\rm tot}=\frac{\int _{t_0}^{t} X_{{\rm NO}_{\rm x}}(\tau )\,p_{\rm tot}(\tau )\,{\dot{n}}(\tau )\,d{ \tau }}{\int _{t_0}^{t}p_{\rm tot}(\tau )\,{\dot{n}}(\tau )\,d\tau }. \end{aligned}$$

(5)

The resulting integral reference concentration diverges from the one based on the unaltered bulk mass flow in that the pressure decrease during the early expansion phase mitigates the maximum ${\rm NO}_{\rm x}$ concentrations while the diminishing influence of dilution is less pronounced due to the lower pressures during the purge phase. This does not incorporate the effect of the considerable velocity variations that could cause additional sample flow fluctuations due to possible changes in stagnation pressure at the sample probe inlet. Momentary changes of pressure at the sampling location could skew the resulting concentration measurements depending on the instantaneous bulk gas state.

As a consequence from these considerations, the integrity of the PDC gas sampling setup needed to be verified. For this purpose, measurements were carried out that involved the pulsed injection of inert gas into a PDC with a continuous air mass flow of ${36.1}\,\hbox {g/s}$. The inert gas used was a mixture of 25% ${\rm {CO}}_{2}$ in Argon. Pulse frequencies of ${2}\,\hbox {Hz}$, ${10}\,\hbox {Hz}$ and ${20}\,\hbox {Hz}$ as well as steady injection were realized. During operation, the time-averaged mass flow of the inert gas as well as the air mass flow was recorded using a Coriolis mass flow meter upstream of the mixing section, as depicted in Fig. 4. These measurements allowed for the determination of the expected ${\rm {CO}}_{2}$ concentrations in the exhaust gas, which could then be compared to the measured concentrations in the gas sample. Injection pressure $p_{\rm inj}$ was varied across a wide range to ensure that it had no influence on the comparability of injected to measured concentrations. The results are shown in Fig. 6a, with $p_{\rm inj}$ being directly proportional to the injection mass flow of the ${\rm {CO}}_{2}$–Ar mixture. To allow for an assessment of the experimental uncertainties involved in this calibration, error bars of the mass flow measurement (black lines) denote mass flow fluctuations² during the measurement, whereas error bars for the concentration measurements (colored lines) derive from the measurement uncertainties as specified for each device.

Fig. 6

Measured and expected $\hbox {CO}_2$ volume fractions with error bars signifying measurement uncertainty for gas analyzer measurements and cyclic fluctuations for mass flow measurements

Agreement is very good, with maximum deviations between mass flow and concentration measurements in the range of 3 to 5% of the measured value, independent of injection pressure and operating frequency. These deviations are fully covered by the uncertainties deriving from flow fluctuations and measurement uncertainty.

To also assess the impact of combustion reactions and shock waves on the sampling system, additional measurements with a mixture of 20% ${\rm {CO}}_{2}$ in ${\rm H}_{{2}}$ were conducted. Analogous to the inert experiments, the mixture was injected into a constant stream of air at varying frequencies. However, the mixture was ignited after filling of the combustion tube was complete. To allow for a combustible mixture, air mass flow rate had to be reduced to ${22.2}\,\hbox {g/s}$ while injection pressure $p_{\rm inj}$ had to be increased. This made operating frequencies above ${10}\,\hbox {Hz}$ unfeasible.

As before, measured ${\rm {CO}}_{2}$ concentrations in the exhaust were compared to measurements of the inflow rates of air and ${\rm {CO}}_{2}$–${\rm H}_{{2}}$obtained by the Coriolis mass flow meters. The depicted results in Fig. 6b show very good agreement within the the range of uncertainty for both ${2}\,\hbox {Hz}$ and ${10}\,\hbox {Hz}$ operating frequencies. Hence, confidence is lent to the fact that the sampling system itself, although only able to capture integral values, delivers representative data about the composition of the exhaust gas, even for pulsed combustion operation of increased frequency. However, it should be noted that due to the diluting influence of ${\rm {CO}}_{2}$  the majority of the combustion events of which the results are shown in in Fig. 6b were fast deflagrations, not detonations. Nevertheless, those still led to the formation of shock waves of significant strength in any case.

2.3 Experimental Parameter Space

The goal of this study is to cover a wide range of possible factors influencing emission values measured from a PDC. This section briefly describes the parameter space of the study. Table 1 gives an overview of the constant and varied operating conditions, along with their default values.

Table 1 Experimental parameters (defaults in boldface)

PDC operating frequencies f of ${2}\,\hbox {Hz}$, ${10}\,\hbox {Hz}$, and ${20}\,\hbox {Hz}$ were chosen for the experiments. However, some configurations did not allow for all frequencies to be investigated, especially in cases where higher frequencies resulted in emission levels outside of the measurement range of the analyzing equipment or when lower operating frequencies resulted in concentrations at the lower end of the resolvable concentration scale. Air mass flow ${\dot{m}}_{\rm air}$, fuel and equivalence ratio $\phi$ were kept constant throughout this study, but their influence is the focus of on-going work.

The first preliminary experiments were targeted towards assessing the necessary experimental run time $t_{{\rm run}}$ to reach steady state conditions in terms of the chemical composition of the measured exhaust gas. Thus, the PDC run time was varied while also analyzing the influence of operating frequency. Critical measurement data to be investigated in that regard consisted primarily of the transient evolution of the measured species mole fractions (${\rm NO}_{\rm x}$, ${\rm O}_{{2}}$, H₂) during the run duration. The measured detonation velocities were taken as confirmation that all shots within one measurement run were indeed successfully induced detonations. This is important as it has been observed that every disturbance in the mode of combustion (e. g. misfirings, unsuccessful DDT) is immediately reflected in the measurement of ${\rm NO}_{\rm x}$ concentrations.

The default fuel injection period ($t_{{\rm fill}}$) during each cycle was set to ${35}\,\hbox {ms}$, which is sufficient to fill the entire PDC tube with combustible mixture prior to ignition. To prevent flashback, a delay of ${5}\,\hbox {ms}$ was employed before ignition to allow an air buffer between the filling section and the actual combustion zone. The impact of varying $t_{{\rm fill}}$ on measured gas species concentrations was investigated.

The choice of a specific sampling time window ${\varDelta } t$ during each PDC cycle could be necessary, especially for low operating frequencies that allow for more flexible sampling timings due to the extended duration of a single detonation cycle. If $t_{{\rm fill}}$ is held constant, lower frequencies experience increased dilution of the gas sample by the longer sampling of purge air in the exhaust. Due to the valveless nature of the combustion chamber air supply, the contact surface between combustion products and purge air within the detonation tube is subject only to the internal flow field and thus depends on the individual pressure development during and after each detonation. As a result, the noticeable onset of the purge phase might change between cycles, possibly altering the overall emission behavior. Therefore, it could be desirable to define a repeatable measurement window during the combustion cycle while still obtaining a sufficiently large amount of sample gas.

Other experiments investigated the influence of the proximity of the sampling location to the combustion chamber outlet. These different geometries are referred to as the step design, the short insert, and the long insert and can be seen in Fig. 3. The step design involves a sudden step-like increase of the detonation chamber’s diameter from 30 to ${40}\,\hbox {mm}$, ${35}\,\hbox {mm}$ upstream of the sampling probe’s inlet. The second one uses a short insert to maintain a constant inner diameter of ${30}\,\hbox {mm}$ until the tube opens towards the environment (${35}\,\hbox {mm}$ downstream of the sampling probe). The third one extends the tube by ${230}\,\hbox {mm}$, thus increasing the distance between sampling point and tube exit. The distance between the point of fuel injection, the ignition location, and the sampling location all remain the same for all three geometries.

The cylindrical sampling probe also allowed for a variation in the alignment of the main flow within the combustion chamber and the orifice of the gas sampling probe, so that the bulk flow velocity of the gases would approach the probe in a different angle $\alpha$.

Finally, the geometry of the probe itself was changed to less intrusive designs such as a pitot tip and a flush mounted design, allowing for an estimation of the impact of a blunt body shape on the high velocity flow downstream of the detonation front with respect to emission measurements.

3 Results and Discussion

Experimental measurements were conducted to investigate the significance of the parameters discussed in the previous section with regard to emissions measurements. Measurements for each configuration were repeated three times, the mean value of which is shown as a solid line or markers while the resulting standard deviation between repetitions is indicated by error bands or error bars. To ensure a wider comparability of the measured ${\rm NO}_{\rm x}$ concentrations and account for different amounts of air dilution of the combustion exhaust gases as discussed in the previous section, these concentrations are additionally displayed when corrected to a fixed exhaust oxygen concentration. For stationary gas turbines and similar systems, this is commonly chosen to be 15 vol% on a dry basis (European Council 2010; U.S. Environment Protection Agency 1993). Additionally, excess ${\rm H}_{{2}}$ in the exhaust gas was mathematically removed as well. However, due to the ${\rm H}_{{2}}$ analyzer being limited to a span of 2%vol, the latter becomes less reliable for large quantities of ${\rm H}_{{2}}$. The full formula for correcting the measured concentrations to reference conditions thus becomes

$$X_{\mathrm {corrected}} = {\frac{20.94 - {\rm O}_{2, {\rm ref}}\%}{20.94-{\rm O}_2\%}}{\frac{100}{100-{{\rm H}_2{\rm O}}\%}} {\frac{100}{100- {{\rm H}_2} \%}}X_{\rm uncorrected}$$

(6)

Note that results reach a singularity when oxygen content in the exhaust approaches atmospheric conditions (that is, for high dilution rates or low operating frequencies). Thus, it becomes very sensitive to small fluctuations in measured ${\rm O}_{{2}}$ concentrations for these cases, which results in measurement uncertainties that become very large. Corrected concentrations are indicated as ${\rm NO}^{{15}{\%}}$ and ${\rm NO}_{\rm x}^{{15}{\%}}$.

3.1 Reaching Steady State Conditions

Due to the differences in operational time scales discussed in the previous section, the interaction of a fluctuating PDC exhaust gas flow with a subsequent CEM is to a certain extent unknown. Therefore, the first task in the course of this study was to investigate the response time of the sampling system and identify the settling time of the combined sampling train and the analyzers for several PDC operating frequencies to ensure that each experimental configuration was able to provide unambiguous results in terms of emission measurement. Figure 7 shows the temporal development of the measured ${\rm NO}_{\rm x}$ concentrations, normalized by the measured value averaged between 60% and 93% of each run time for varying operating frequencies and PDC run times.

Fig. 7

${\rm NO}_{\rm x}$ concentrations normalized by their approached steady state value over time $\hbox {NOx}_{,\mathrm {end}}$ for varying PDC run times

Notable differences in the rise behavior of the signal can be found that result from the strong dependence of measured ${\rm NO}_{\rm x}$ concentrations on the operating frequency: While ${10}\,\hbox {Hz}$ and ${20}\,\hbox {Hz}$ result in rise rates in excess of the sensor response time, leading to identical initial surges followed by a more moderate adjustment period to the final steady-state value, the overall signal for ${2}\,\hbox {Hz}$ is a lot smoother. Another result of this behavior is the fact that measured ${\rm NO}_{\rm x}$ values tend to initially overshoot for the cases of 20 Hz and undershoot for ${10}\,\hbox {Hz}$. Nevertheless, all examined frequencies provide sufficiently stable ${\rm NO}_{\rm x}$ concentrations for run times of ${20}\,\hbox {s}$ and ${30}\,\hbox {s}$, in the sense that relative temporal standard deviation during the averaged steady-state time window was reduced to below 1%, which is of the same scale as the accuracy of the CLD analyzer. The relative spread of the results is mostly constant across the investigated frequencies, with a slight increase for the ${2}\,\hbox {Hz}$ case due to the reduced signal strength for lower concentrations.

Sufficiently steady signals must also be ensured for the measurement of ${\rm O}_{{2}}$ through the paramagnetic sensor in order to correct for the exhaust ${\rm O}_{{2}}$ concentration.

Figure 8 shows the measured ${\rm O}_{{2}}$ volume fractions over time, again for varying PDC run times and operating frequencies. The most important information to be derived from Fig. 8 is the fact that all curves obtained for the same operating frequency coalesce towards a common, stable oxygen volume fraction, independent of run time (indicated by dotted black lines). However, reaching this value requires considerably more time compared to the ${\rm NO}_{\rm x}$ signal due to the fact that the paramagnetic sensor is located farther downstream of the sample line (larger volume) and also has a longer response time. For this reason, the sensor does not report any change in composition until approximately ${10}\,\hbox {s}$ of PDC run time have already elapsed, independent of frequency or total run time length.

Fig. 8

Time development of measured ${\rm O}_{{2}}$ volume fraction for varying PDC run time

Due to less sampled purge gas over the course of a cycle at different operating frequencies, a clear frequency dependence is also visible, with the oxygen content of the exhaust gas reaching a minimum for the highest operating frequency.

Also, a sudden jump in the measured oxygen content is apparent at the start of the PDC operation ($t={0}\,\hbox {s}$) and at the end of each run (at $t={10}\,\hbox {s}$, $t={20}\,\hbox {s}$, and $t={30}\,\hbox {s}$). These jumps are the result of strong vibrations induced to the casing of the gas analyzer by pressure waves leaving the combustor during the operating time of the PDC and thus mark their onset and conclusion during the course of a run. Because the paramagnetic ${\rm O}_{{2}}$ sensor is of the magnetomechanical type, its inner test body is susceptible to vibrations that can cause oscillations and thus indicate a change in oxygen content. Depending on the frequency, this error can indicate an increase or decrease in ${\rm O}_{{2}}$, as can also be found in Fig. 8. Nonetheless, since measured oxygen concentrations between varying operating time (i. e. exposure time to vibrations) agreed remarkably well and no noticeable drift in the baseline value could be found, it can be concluded that this shift is only temporary in nature and has no lasting effect on the measurement result, as long as care is taken in the choice of a time frame that omits this behavior. Thus, only the resultant stable oxygen values after PDC operation has ceased were considered to determine the oxygen content of each sample (indicated by the horizontal dotted lines in Fig. 8).

Similar to the requirements with regard to a minimized fluctuation of the measured ${\rm NO}_{\rm x}$ and NO signals discussed before, a PDC operating time of ${20}\,\hbox {s}$ is typically sufficient to obtain a stable period of measured ${\rm O}_{{2}}$ concentration, after the aforementioned vibrations have stopped. Nevertheless, to ensure that the initial transient behavior found in both measured species concentrations does not affect time-averaged reference values, a PDC operating time of ${30}\,\hbox {s}$ was chosen as the reference values for all the following experiments. A steady-state reference value for each configuration was derived by taking a time-average of the measured signal between ${18}\,\hbox {s}$ and ${28}\,\hbox {s}$ after the initial rise in ${\rm NO}_{\rm x}$ (${21}\,\hbox {s}$ and ${31}\,\hbox {s}$ for ${\rm O}_{{2}}$ due to the additional delay). It is worth pointing out that these numbers are specific to the experimental setup and should be adjusted if changes in the laboratory configuration—such as the distance between devices—are made. Researchers are therefore encouraged to independently confirm their own system specific response and settling time.

3.2 Influence of Operating Frequency

Figure 9 shows the measured concentrations of ${\rm NO}_{\rm x}$ in absolute terms, as well as corrected to an oxygen content of 15% on a dry basis. As for the oxygen content, measured ${\rm NO}_{\rm x}$ emissions strongly depend on the chosen operating frequency for uncorrected concentrations. Since all frequencies were operated using the same fuel injection timing, and thus primarily differ in the amount of purge air between ignitions, this is to be expected. Figure 9 confirms that this dependence is indeed linear for absolute ${\rm NO}_{\rm x}$ measurements.

Fig. 9

Sample average of measured NO_x concentrations for varying PDC operating frequency

When corrected to 15% ${\rm O}_{{2}}$, the differences between the operating frequency are greatly reduced. This is reassuring and agrees with with the observations in Fig. 6 that the system can reliably capture integral values, and the observed variations in the following sections are primarily due to sampling effects and not integration effects. As mentioned at the end of Sect. 2.2, oxygen correction amplifies the measurement scatter for ${2}\,\hbox {Hz}$ due to the large ${\rm O}_{{2}}$ content of the exhaust gas.

Figure 9 also shows NO concentrations measured parallel to ${\rm NO}_{\rm x}$, which indicates that the measured ${\rm NO}_{\rm x}$ consists mostly of NO. Although the influence of the sampling method on the NO oxidation could not be quantified, this is in agreement to the findings of Yungster et al. (2006). There, only negligible amounts of ${\rm {NO}}_{2}$were found inside the combustion tube, with the bulk of the observed ${\rm {NO}}_{2}$ formed outside in the direct vicinity of the PDC exhaust after the ejected NO mixed with the surrounding air. Therefore, since ${\rm NO}_{\rm x}$ and NO concentrations can be considered close to equivalent in the conditions found inside the PDC, the remaining analysis will focus on measurement values for ${\rm NO}_{\rm x}$.

3.3 Outlet Geometry

Ideally, the gas sample to be analyzed for pollutant levels should be taken at a position where fuel consumption is completed and that allows for consistent measurement of exhaust gas composition. However, due to the transient nature of the detonation cycle, gas dynamic effects such as reflected shock waves, rarefaction waves, and temporary back flow could influence the exhaust gas composition at the sampling probe location. This section therefore investigates three distinctive outlet configurations: step configuration, short insert and long insert, which have been introduced in Fig. 3.

Figure 10 shows the results of ${\rm NO}_{\rm x}$ measurements for these configurations for PDC operating frequencies of ${2}\,\hbox {Hz}$ and ${10}\,\hbox {Hz}$. Since an operating frequency of ${20}\,\hbox {Hz}$ resulted in measured ${\rm NO}_{\rm x}$ concentrations above the upper limit of the CLD (${2500}\,\hbox {ppm}$), these results are not shown. It becomes obvious that the interaction of probe positioning and outlet geometry can have a significant impact on the measured ${\rm NO}_{\rm x}$ emissions. This is the case for both measured and oxygen-corrected results.

Fig. 10

Sample average of measured concentrations and sample mean pressure for varying outlet geometry

When measuring with the short insert installed instead of the step design, an increase in ${\rm NO}_{\rm x}$ in Fig. 10a is accompanied by an increase in sample line mean pressure in Fig. 10c as well as by a noticeable decrease in oxygen and hydrogen in Fig. 10b (the latter only for $f={2}\,\hbox {Hz}$). The increase in mean pressure is a result of the combination of higher static pressure and increased dynamic pressure on the leading edge of the probe due to the elimination of the sudden expansion.

The gas sample collection is primarily defined by the instantaneous pressure difference between sample pump and combustion chamber. An increase in mean sample line pressure would therefore indicate an increase in mean sample mass flow. However, since the pressure increase is caused by additional kinetic energy of the gas, it is more likely to increase the sample rate only during periods of high flow velocity. These periods primarily consist of the detonation and subsequent exhaust stage of the PDC cycle before purge, which are also the stages of highest ${\rm NO}_{\rm x}$ concentration inside the tube. However, this should also result in a corresponding decrease in measured ${\rm O}_{{2}}$ and ${\rm H}_{{2}}$  which would compensate for any additionally measured ${\rm NO}_{\rm x}$ when oxygen corrected values are employed. Although a slight decrease in ${\rm O}_{{2}}$ and ${\rm H}_{{2}}$ is observable, it is insufficient to explain the increase in measured ${\rm NO}_{\rm x}$ by the above mentioned phenomenon.

This implies that higher measured ${\rm NO}_{\rm x}$ does not solely result from unsteady sampling but could also be a result of a change in the state of the combusted gases before entering the sampling probe due to the change in outlet geometry. The sudden change in cross section interferes with every shock and expansion wave propagating across. Combustion products flowing downstream due to the expansion occurring after the detonation has left the tube are subject to a sudden pressure decrease when crossing the step. This potentially leads to a change in volume bias of the integral sample volume, which was shown before to be dependent on the pressure in the vicinity of the sampling probe. Slightly increased oxygen content for the step design in Fig. 10b and lower pressures in Fig. 10c match this observation, but could also signify the sampling of back flowing ambient gases or separation regions, which would be in line with the marked increase in sampled hydrogen for the ${2}\,\hbox {Hz}$ case with the step design.

When comparing the results for the short and long insert, differences in emissions are not as large as for the step design. It has been shown in several studies that back flow of surrounding gases can occur during filling of the PDC (Hoke et al. 2006) as well as during the exhaust stage (Caswell et al. 2013). Since the influence of these back flows is more pronounced in the direct vicinity of the tube’s exhaust and reaches the sampling location earlier if it is placed nearby, employing the long insert configuration should reduce possible errors in gas composition measurements. However, a potentially more important effect derives from the additional overall length of the combustion tube for the long insert. As a result, expansion waves in the wake of the detonation require more time to reduce pressure and temperature inside the combustion chamber and further accelerate the combustion products towards the exhaust. Thus, the residence time of these products at elevated pressures and temperatures is increased, leading to increased ${\rm NO}_{\rm x}$ concentrations. This effect has also been discussed in detail in Yungster et al. (2006), where a continuous, albeit nonlinear increase of NO was seen for increased tube length.

Concluding from these observations, the influence of the outlet geometry on the composition of the sampled exhaust gas should not be underestimated. A sudden change in the combustion chambers geometry was shown to have a significant impact on measured ${\rm NO}_{\rm x}$ concentrations. However, due to multiple possible interactions with the flow field and the combustion products during the PDC cycle, this effect is hard to quantify and such geometries should therefore generally be avoided. For a constant tube diameter, the residence time of the combustion products at elevated pressures and temperatures is governed to a large extent by the time required for the expansion waves emerging from the open end to reach the combustion products. Thus by changing the distance between the gas sampling location and the combustion tube exit, an increase in measured ${\rm NO}_{\rm x}$ concentrations for longer tubes is observed. However, in addition to this more replicable effect, interference of the exhaust in the form of back flow and ambient air dilution can not be fully ruled out, which is why the long insert was chosen as the reference for subsequent emission measurements. This had the additional benefit of reducing the vibrational strains to the analyzing equipment (in particular the paramagnetic sensor, as mentioned in Sect. 3.1) by leading the exhaust pressure waves away from the measurement equipment. Future researchers should therefore endeavor to position their sampling probes far from such sudden expansions while also avoiding comparisons between measurements with significantly different downstream tube lengths (or at a minimum account for the differences in the blowdown times).

3.4 Fill Time

Some aspects of the impact of fuel charge length on ${\rm NO}_{\rm x}$ emissions have already been discussed in Yungster et al. (2004, 2006), where charge length was varied by using combustion tubes of different lengths. For multi cycle operations with a fixed tube length, altering the fill time $t_{{\rm fill}}$ primarily changes the ratio of combustible gases to purge gases during one cycle. As already listed in Table 1, the current setup was operated with a constant air mass flow of ${36.1}\,\hbox {g/s}$, which requires an additional ${1.055}\,\hbox {g/s}$ of hydrogen to be injected for stoichiometric combustion. This is equivalent to a mean flow velocity of ${60}\,\hbox {m/s}$. Since the overall test rig length including the DDT section and the long insert is ${1.75}\,\hbox {m}$, a fuel injection period of ${35}\,\hbox {ms}$ has been used for the discussion so far, which results in a slight overfilling of the tube.

Figure 11 now investigates the resulting changes in measured gas composition if $t_{{\rm fill}}$ is altered for the long insert configuration at an operating frequency of ${10}\,\hbox {Hz}$. The apparent effect of reducing the fill time to ${20}\,\hbox {ms}$, and thus shortening the charge length, is to simultaneously reduce the ratio of combustion gases to purge air and to lower the combustion energy released with every cycle, because the detonation wave now only propagates through 2/3 of the overall tube before it decays to a pressure wave. This is in accordance with an increase in measured ${\rm O}_{{2}}$ and decrease in measured ${\rm H}_{{2}}$. Uncorrected ${\rm NO}_{\rm x}$ concentration decreases, for the most part due to the air dilution, but some additional effects have to contribute as well.

Fig. 11

Sample average of measured concentrations and pressure increase for varying $t_{{\rm fill}}$ at $f={10}\,\hbox {Hz}$

The most prominent effect of increasing or decreasing $t_{{\rm fill}}$ is to alter the ratio of fill time to purge time. Increasing $t_{{\rm fill}}$ should result in an increase in measured ${\rm H}_{{2}}$ and a decrease in measured ${\rm O}_{{2}}$, which is confirmed in Fig. 11b. Since ${\rm O}_{{2}}$ volume is thus effectively replaced by ${\rm H}_{{2}}$  oxygen-corrected ${\rm NO}_{\rm x}$ values decrease in Fig. 11a and no longer provide a meaningful comparison, because Eq. 6 is only valid for small traces of ${\rm H}_{{2}}$ in the exhaust gas. While ${\rm H}_{{2}}$ values in Fig. 11b appear to only exceed the upper limit of the analyzer of 2%vol for the longest fill time, short phases of sensor saturation that would distort the measurement result can be obscured by its cycle-averaged nature. This can be considered a general problem for any sort of post-process correction of emission measurements in cyclic combustion and it should therefore be ensured that no unknown gas quantities can distort measurements during operation.

Overall, the additional volume of ${\rm H}_{{2}}$ that is brought into each combustion cycle during the prolonged filling time causes ${\rm NO}_{\rm x}$ concentrations to decrease. The slight increase in total ${\rm NO}_{\rm x}$ from 35 to ${50}\,\hbox {ms}$ in Fig. 11a could be caused by transient effects at the beginning of the fill time: Since the fuel injectors used in this study operate at a high upstream pressure, initial ${\rm H}_{{2}}$ mass flow is larger as the pressure first needs to decrease before steady state conditions are reached after a few $\hbox {ms}$. This behavior is visible when investigating the fuel supply pressure upstream of the fuel injectors in Fig. 11c. After opening of the injectors, the sharply decreasing pressure requires a few milliseconds until a steady discharge pressure is reached. Since the momentary fuel mass flow into the combustion tube is directly linked to the supply pressure, this behavior leads to slightly richer mixtures at the tip of the package of combustible gas. As can be seen, increasing $t_{{\rm fill}}$ to ${50}\,\hbox {ms}$ shifts this transient zone further away from ignition, causing the affected mixture to exit the combustion tube before the onset of detonation. The fuel remaining inside the tube would display an overall more homogeneous axial distribution, rendering the mixture more stoichiometric and thus resulting in increased total ${\rm NO}_{\rm x}$ emissions.

3.5 Sampling Time Variations

Fig. 12 depicts a PDC cycle of duration ${\varDelta } T$ as experienced by a sampling probe inside the tube to illustrate the possible impact of the chosen sample time window. Each cycle is composed of a filling phase $t_{{\rm fill}}$ containing the stoichiometric ${\rm H}_{{2}}$–Air mixture, the combusted products that contain all the ${\rm NO}_{\rm x}$, and a subsequent purging state where the products are replaced by fresh air. The approximate time resolved ${\rm NO}_{\rm x}$ curve depicted in Fig. 12 is derived from the same one-dimensional simulation of a detonation wave that has been used in Fig. 5b and illustrates the inhomogeneous axial distribution of ${\rm NO}_{\rm x}$ within the combustion products. This distribution is not only caused by differences in ${\rm NO}_{\rm x}$ concentration throughout the detonation cycle, but also by the fact that gas pressure and density are time dependent, with a maximum shortly behind the shock wave and a rapid decline once the exhaust stage sets in. It is easy to imagine that, by altering the sampling period ${\varDelta } t=t_{\mathrm {end}}-t_{\mathrm {start}}$ and timing within this cycle, either by delaying the beginning of $t_{\mathrm {start}}$ or by ending it earlier at $t_{\mathrm {end}}$, the outcome of the measurement of the ${\rm NO}_{\rm x}$ concentration can be influenced. However, in what way this influence is reflected in the measured concentrations is unclear and is the scope of this section.

Fig. 12

Schematic temporal development of exhaust gases sampled by the probe for varied sample times

The sampling time variation is experimentally realized by employing a switching valve downstream of the sampling probe (see Fig. 4) that allows the probe to sample inert gas consisting of 25% C${\rm O}_{{2}}$ in Ar instead. This allows for maintaining a sufficient flow rate within the analyzing section as well as to measure the concentration of dilution gas (by measurement of the resulting C${\rm O}_{{2}}$ concentration).

Figure 13 summarizes the findings from altering sampling start and end time, by comparing the resulting ${\rm NO}_{\rm x}$ values for operating frequencies of ${2}\,\hbox {Hz}$ and ${10}\,\hbox {Hz}$. Total measured ${\rm NO}_{\rm x}$ concentrations are normalized by the result for a continuous sampling throughout the detonation cycle, i. e. ${\varDelta } t={\varDelta } T$. The measured C${\rm O}_{{2}}$ volume fraction is used as an indicator for the amount of inert gas dilution. The latter was measured both for the dry and the wet line of the gas analyzer section, where values on a dry basis are necessarily higher due to the water vapor removal, thus also providing information about the sample’s water content.

Fig. 13

Influence of sample time variation on gas composition, ${\rm NO}_{\rm x}$ emissions normalized by full sample result

By looking at Fig. 13a it can be observed that delaying the sampling start while keeping $t_{\mathrm {end}}={\varDelta } T$ causes an initial increase of measured ${\rm NO}_{\rm x}$ by roughly 20%, followed by a steep decline for all cases where sampling only started after ignition had already occurred. The decline is plausible, because gas with high ${\rm NO}_{\rm x}$ concentration and high pressure is effectively omitted from each cycle’s gas sample.

The increase in ${\rm NO}_{\rm x}$ for sample start times between ${10}\,\hbox {ms}$ and ${20}\,\hbox {ms}$ was initially unexpected. Essentially, delaying sampling from the combustion chamber during fill time replaces combustible mixture with the inert Ar–${\rm {CO}}_{2}$ mixture in the overall sampled gas volume for each cycle. Since both mixtures should not contain any ${\rm NO}_{\rm x}$, the observed increase can only be caused by a decrease of the total sample mass, rendering the relative amount of sampled ${\rm NO}_{\rm x}$ larger. This implies that the omitted ${\rm H}_{{2}}$–air mixture is not equivalently replaced by the inert gas. One explanation for this was found by analyzing the ${\rm {CO}}_{2}$ content of the measured gas in Fig. 13b, where a noticeable increase of ${\rm {CO}}_{2}$ in the gas sample is only seen for inert sampling times $>0.2{\varDelta } T$. This is most likely caused by the finite response time of the switching valve, leading to neither combustion gases nor inert gas being drawn into the analyzing section for the first ${20}\,\hbox {ms}$ of each combustion cycle. An instantaneously reacting switching valve would result in measured ${\rm {CO}}_{2}$ volume fractions following the dashed line, displaying a fully linear dependence from a sample containing 0% up to 100% of inert gas.

However, results for reduced sampling times by decreasing $t_{\mathrm {end}}$ that are displayed in Fig. 13c indicate that valve response time alone can not be responsible for the change in overall sample mass when switching to inert gas during the combustion cycle. Since ${\varDelta } T$ is frequency dependent, the influence of $t_{\mathrm {end}}$ is shown only relative to ${\varDelta } T$ for both frequencies. A simple linear relation is found for $t_{\mathrm {end}}>0.2 {\varDelta } T$, with increasing ${\rm NO}_{\rm x}$ concentrations for larger time periods of inert gas sampling. Even for measurements where combustion gases were drawn in only during the first 20% of each cycle, measured ${\rm NO}_{\rm x}$ concentrations continued to rise when inert gas sampling was increased further. The results of Fig. 13a have already shown that ${\rm NO}_{\rm x}$ formation is tied very strongly to the very short time frame of the propagating detonation wave and thus ${\rm NO}_{\rm x}$ content of any ensuing gas flow can be neglected. So, as before, an increase in measured ${\rm NO}_{\rm x}$ concentration when switching from one low-${\rm NO}_{\rm x}$ source to another can only be explained by a simultaneous decrease in overall sample mass. But as was shown in Fig. 13b, ${\rm {CO}}_{2}$ content was already significant for these configurations, meaning that inert gas was clearly being collected by the analyzing system. This likely means that, even though it is collected by the sampling system, the mass of inert gas is unable to equivalently replace the gases that would otherwise be drawn from the combustion chamber during that time. This is a clear indication that (as was already argued in Sect. 2.2) the pressure increasing nature as well as the instationary flow field have a significant impact on the sampling process itself by influencing the momentary sampling mass flow.

Thus, constraining the sample time during the PDC cycle is only a viable option if the omitted gas volume is equivalently replaced by inert gas or the change in integral sample mass can be quantified in some way. Due to the strong influence of the instationary flow field of the PDC cycle on the sample mass flow, these requirements are hard to fulfill and a distortion of measured pollutant concentrations is therefore likely.

3.6 Sampling Probe Orientation

Switching between gas from the PDC cycle and inert purge gas in the last section has shown that the flow conditions in unsteady combustion systems like the PDC can influence the outcome of emission measurements. It can be expected that the fluctuating pressure field in the vicinity of the sampling probe in particular, resulting from static pressure changes as well as from the dynamic pressure of varying mass flows during each cycle, plays a major role in defining the momentary sample mass flow though the probe. The severity of this influence would thus also depend on the orientation of the sampling probe inlet relative to the bulk flow. Figure 14 depicts the inlet of a cylindrical probe that can be rotated in such a way that the angle between the inflowing gas velocity and the sampling orifice can be varied. Investigated angles were ${0}^{\circ }$ (inlet at stagnation point, default configuration), ${45}^{\circ }$, ${90}^{\circ }$ and ${180}^{\circ }$, as shown in Fig. 14.

Fig. 14

Investigated angles for cylindrical probe in turbulent flow

In Fig. 15, temporal development of measured ${\rm NO}_{\rm x}$ fractions over a PDC run time of ${30}\,\hbox {s}$ is shown for operating frequencies of ${2}\,\hbox {Hz}$ and ${10}\,\hbox {Hz}$ and varied probe inlet angles. For both frequencies, increasing the angle results in a small increase in measured ${\rm NO}_{\rm x}$ for ${45}^{\circ }$ and a decrease for larger angles. For ${10}\,\hbox {Hz}$, this decrease is very significant and is accompanied by a change in the temporal behavior, where ${\rm NO}_{\rm x}$ values initially overshoot and then continuously decline towards a lower steady value.

Fig. 15

Time development of measured ${\rm NO}_{\rm x}$ concentration for varying PDC operating frequency and sample probe inlet’s angle to flow direction

Mean ${\rm NO}_{\rm x}$ values from Fig. 15 together with the corresponding oxygen corrected data is shown in Fig. 16. Apart from the already discussed decrease in measured ${\rm NO}_{\rm x}$, it can be seen that differences for oxygen corrected ${\rm NO}_{\rm x}$ between operating frequencies increases for larger angles.

Figure 16 sheds some light on the distinctly different behavior for larger flow angles at ${10}\,\hbox {Hz}$ operating frequency: It depicts the absolute pressure measured at the inlet of the CLD analyzer before and during PDC operation. In accordance with the assumed flow field of Fig. 14, the initial pressure, which is purely induced by the total pressure resulting from the constant air flow before PDC operation begins, is highest for ${0}^{\circ }$ where it is increased by the dynamic pressure of the flow. It is lowest for ${90}^{\circ }$, where no stagnation occurs in the vicinity of the sampling probe inlet. During the cycle stages of high gas velocity (detonation propagation and exhaust) the accelerated flow increases the pressure for the forward facing orientations, while decreasing that of the perpendicular and rear-ward facing orientations. This implies that the strong variations in pressure and velocity inherent to the detonation cycle increase the static pressure in the vicinity of the stagnation point on the leading edge of the probe and decrease the pressure along the leeward side of the separated flow. Since the sample mass flow is driven by pressure difference, altering this difference by changing the probe orientation aligned with transient pressure changes during every detonation cycle will alter the resulting proportion of gas sampling. It can be safely assumed in this case that the vacuum indicated in the sample line for angles $>{45}^{\circ }$ only occurs during the times of highly accelerated gas flow after the passing of the detonation front and expansion of the combusted gases. Since this is also the period of highest ${\rm NO}_{\rm x}$ concentration within the combusted gases, this attributes to the decrease in measured ${\rm NO}_{\rm x}$ for these cases.

It is worth noticing that an inlet angle of ${45}^{\circ }$ results in the highest uncorrected ${\rm NO}_{\rm x}$ measurements for both operating frequencies, while correcting to 15% ${\rm O}_{{2}}$ moves concentrations below those recorded for an inlet angle of ${0}^{\circ }$. This is caused by a significantly higher measured ${\rm O}_{{2}}$ content for the case of ${0}^{\circ }$, which indicates the increased sampling of purge air compared to the ${45}^{\circ }$ configuration.

Fig. 16

Measured ${\rm NO}_{\rm x}$ for varying probe inlet angle and CLD inlet pressure (for $f={10}\,\hbox {Hz}$)

3.7 Sampling Probe Design

The original cylindrical probe design, which had been chosen due to its robustness and ease of thermal control, had the downside of being rather intrusive with regards to the chamber flow field due to its high blockage ratio. Due to the large impact of the flow field on the sampling flow and by that on the measured concentrations that was found in the previous sections, it can be expected that the geometry and orientation of the probe in the measurement region can impact the measured concentrations. Thus, in addition, a pitot tube probe and a probe mounted flush with the combustion chamber wall were tested using the long insert outlet configuration and a PDC operating frequency of ${10}\,\hbox {Hz}$. The resulting ${\rm NO}_{\rm x}$ concentrations are presented in Fig. 17, where they are compared to results obtained using the cylindrical probe. Additionally, ${\rm O}_{{2}}$ and ${\rm H}_{{2}}$ volume fractions and CLD inlet pressures are compared for all designs under the same operating conditions.

The measured ${\rm NO}_{\rm x}$ emissions for the pitot and flush mounted probes are markedly lower compared to the cylindrical probe for uncorrected and oxygen corrected data in Fig. 17a, while oxygen content remains almost unchanged (Fig. 17b). When comparing the CLD inlet pressure in Fig. 17c, distinctive differences are observable: Due to its high blockage ratio, the cylindrical probe experiences a static pressure increase before operation of the PDC commences. Pressure increases again during PDC operation. The flush mounted probe shows hardly any change in pressure during operation. Initial static pressure at the CLD inlet is slightly reduced for the pitot probe, which is caused by the increased flow resistance of its small, bend tip. During operation, flow resistance increases further due to the heating up of the tip, which further decreases sample line pressure. In contrast to the similar effect discussed in Sect. 3.6, here the pressure decrease occurs gradually over the course of the PDC run time. The primary reason for an increase in pressure for the cylindrical probe would be the significantly higher blockage ratio compared to the pitot tube.

Fig. 17

Measured species concentrations for all three probe designs and CLD inlet pressure (for $f={10}\,\hbox {Hz}$)

Comparing these results with the ones from altering the probe inlet angle in Fig. 16a, it appears that the link found between sample line pressure and measured ${\rm NO}_{\rm x}$ concentrations does not apply to the flush mounted probe, where pressure changes inside the combustion chamber are barely reflected in the sample line pressure and thus have limited influence on the sample mass flow and integral composition. Instead, measured ${\rm NO}_{\rm x}$ concentration is very similar to the case of a cylindrical probe with an opening orifice perpendicular to the main flow, indicating that the reasons for the decreased concentrations are the same as discussed in Sect. 3.6.

Even though variations of pressure are to some extent undesirable for the emission sampling system, it has been shown in Sect. 2.2 that only a sampling mass flow that accounts for the variations inherent to the bulk mass flow is able to produce faithful integral emission values. This is a key difference between the cylindrical and pitot probe designs that collect their sample directly from the bulk flow center line in comparison with the flush mounted probe designs.

4 Summary

It was shown that even a highly unsteady system such as PDC allows for measurement of reasonably steady cycle-averaged emission values if given sufficient time. Dependence on operating frequency for a constant charge length is primarily related to the amount of dilution by purge gas between cycles and can thus be accounted for when correcting for a reference exhaust oxygen content (or similar means, such as considering the emission index), if dilution with ${\rm O}_{{2}}$ is not too high. An equivalently effective measure would be the usage of emission index to indicate emission levels. However, both correction approaches can only account for dilution and are unable to account for the interaction of the sampling probe with the unsteady flow as was discussed above and will be summarized below.

A regular PDC cycle exhibits shock and pressure waves as well as expansion waves. This puts focus on the boundary condition of the detonation tube and possible interactions with a sampling probe if it is placed in the vicinity. To avoid unwanted effects from a change in combustor tube diameter, the sampling probe should be located sufficiently upstream of the combustor exit and far away from any changes in chamber geometry.

Varying fuel fill time and sampling periods can strongly influence emission measurements by altering the overall gas composition as well as the transient process controlling the collection of sample gases during one detonation cycle. Beside changing the composition, varying $t_{{\rm fill}}$ can also influence the axial distribution of equivalence ratio and the momentary flow field inside the detonation tube.

Small changes in sample timing can have a strong impact when these changes interfere with the occurrence of the detonation wave. As predicted in preliminary numerical studies in Hanraths et al. (2018), the bulk of ${\rm NO}_{\rm x}$ is formed directly behind the front. Additionally, since the momentary sampling rate during each PDC cycle is strongly impacted by the flow field inside the combustion chamber, switching to any idle purge gas supply for sampling during the cycle alters the overall sampling volume of which the integrated pollutant concentrations are derived. It thus distorts measurement results in a way that is difficult to quantify and should therefore be avoided.

The results for varying the sample probe inlet angle, as well as the design of the probe, have shown that changes of the flow field in the vicinity of the probe inlet influence sample gas composition. The reasons for this are most likely the combined effect of a change in the driving pressure difference between combustion chamber and analyzer as well as the deflection of the gas around the probe inlet. Naturally, an idealized gas sampling probe from a system with transient mass flow would be non-intrusive. At the same time, it should be able to account for the temporal changes in overall mass flow in the corresponding sample mass flow. This way it could be ensured that measurement would already be mass weighted and thus represent the actual amount of pollutants that was released to the environment. Practically, this would mean that a potentially less intrusive sampling positioning such as the flush mounted sampling probe might not be able to maintain a sufficiently proportional sample mass flow throughout the high velocity phases of the PDC cycle, as indicated by the decrease in measured ${\rm NO}_{\rm x}$ concentrations. On the other hand, the sample line pressure of the flush mounted probe is less affected by pressure changes inside the combustion chamber, which would allow for a more stable sample mass flow, thus simplifying the interaction between combustion chamber and gas sample analyzer.

Fig. 18

Qualitative comparison of the the studied experimental parameters’ impact on measured ${\rm NO}_{\rm x}$ emissions, with and without oxygen correction

Figure 18 summarizes the results of this study by qualitatively showing the severity of the impact of the studied experimental parameters on the measured ${\rm NO}_{\rm x}$ emissions. Also depicted by the dashed lines is how this impact is influenced by oxygen correction of the results.

It becomes clear that a variation of the sampling time should be avoided at all costs. While oxygen correction almost eliminates the frequency dependence of the measurements, its influence on the scale of other uncertainties is limited and it can even have adverse effects in the case of a variation of the probe inlet angle. That said, oxygen correction is overall beneficial and should be always used for emissions comparisons between PDC emissions measurements. Following oxygen correction and a steady, consistent sampling time, the most impactful parameters for researchers are a consistent filling time and probe design. Because these two parameters are likely to also show significant variability between laboratories, it is particularly important for researchers to carefully choose and report these parameters when presenting their results.

Even though this work focused on PDC, in principle, the results can be also applied to other technical applications that involve changes in flow field and chemical reactions on time scales that are irresolvable for subsequent gas analyzing systems. This includes single-cylinder test rigs of spark ignition engines used for the investigation of engine knock (a phenomenon that in itself can be closely tied to detonations in some cases) or per-cycle variations in pollutant emissions from diesel and gasoline engines, which have gathered more interest lately due to more practical reference driving cycles in emission regulations (Karvountzis-Kontakiotis et al. 2017). Here, the definition of a sensible reference value that has to meet regulation values is a crucial topic as well. Pulse jets are another application closely related to PDC in terms of their operating frequencies and air-breathing operation. These conditions can introduce fast-changing flow conditions as well as air dilution that is difficult to quantify, especially when an ejector is applied (Williams et al. 2000). A similar concept, the shockless explosion combustion (SEC) relies on the auto-ignition of a spatially inhomogeneous fuel-air mixture triggered by acoustic pressure waves. Similar to PDC, each pulse jet or SEC operating cycle includes a purge phase to separate hot products from fresh gases, resulting in the same challenges when trying to adequately weight emission levels and maintain comparability with conventional combustion devices. The above discussions of the impact of probe design and positioning, sampling timing, and operating frequency are thus equally applicable and should be considered in the design of experiments and control measures.

5 Conclusion

Although crucial for eventual practical applications, the consideration of pollutant emission characteristics during the development of novel combustion concepts such as PDC is a topic which has not been as intensively discussed as other aspects. This is in part due to the fact that emissions measurements from instationary combustion in general, and pulse detonation combustion in particular, are a challenging task. The main reasons for this are short time scales, uncertainties in the exact state of the gases to be examined during sampling, the slow response of analyzing and sampling equipment, and techniques targeted towards continuous, steady state combustion systems. This study focused on understanding some of these challenges as well as potential sources of measurement error by considering a range of geometric and systematic parameters and their influence on ${\rm NO}_{\rm x}$ emission measurements.

The goal of this work was to investigate and quantify possible impact factors on successful emission measurements from PDC. It was shown that care must be taken in ensuring experimental conditions that ensure a consistent flow interaction of the sampling probe with the unsteady mass flow within the combustion chamber. Practically, this means that small changes in overall geometry as well as the timing of the sample, which in contrast might be irrelevant in the case of stationary combustion, can influence measurement results in a way that is difficult to predict and should therefore be mitigated as much as possible. Fully quantitative comparability would therefore most likely require the development of a model burner with a more controllable, yet also less practical geometry. However, despite the cycle-averaged nature of any emission measurements in the context of PDC, operating conditions such as the frequency of ignition and the amount of purge gas can be accounted for by correcting the measured exhaust values accordingly.

Nevertheless, while absolute emission values retain a certain degree of uncertainty due to individual contributions of the effects summarized above, it has been shown that traditional gas sampling can be used to investigate the impact of changed operating conditions on ${\rm NO}_{\rm x}$ emissions from unsteady combustion when the factors discussed above are considered.