Pere Tuset-Peiró

Francisco Vázquez-Gallego

Jonathan Muñoz
email: jonathan.munoz@inria.fr

Thomas Watteyne
email: thomas.watteyne@inria.fr

Jesus Alonso-Zarate

Xavier Vilajosana
email: xvilajosana@uoc.edu

Experimental Interference Robustness Evaluation of IEEE 802.15.4-2015 OQPSK-DSSS and SUN-OFDM Physical Layers for Industrial Communications

Keywords: IEEE 802.15.4, smart utility networks, OQPSK-DSSS, SUN-OFDM, interference

In this paper, we experimentally evaluate and compare the robustness against interference of the OQPSK-DSSS (Offset Quadrature Phase Shift Keying-Direct Sequence Spread Spectrum) and the SUN-OFDM (Smart Utility Network-Orthogonal Frequency Division Multiplexing) physical layers, as defined in the IEEE 802.15.4-2015 standard. The objective of this study is to provide a comprehensive analysis of the impact that different levels of interference produce on these modulations, in terms of the resulting PDR (Packet Delivery Ratio) and depending on the length of the packet being transmitted. The results show that the SUN-OFDM physical layer provides significant benefits compared to the ubiquitous OQPSK-DSSS in terms of interference robustness, regardless of the interference type and the packet length. Overall, this demonstrates the suitability of choosing the SUN-OFDM physical layer when deploying low-power wireless networks in industrial scenarios, especially taking into consideration the possibility of trading-off robustness and spectrum efficiency depending on the application requirements.

Introduction

The IEEE 802.15.4 standard [START_REF]IEEE Standard for Low-Rate Wireless Networks; IEEE Std[END_REF] was first released in May 2003 and defined a physical layer (PHY) and a MAC (Medium Access Control) layer for WPAN (Wireless Personal Area Networks) operating in the sub-GHz (868 MHz in Europe, 915 MHz in America) and the 2.4 GHz worldwide ISM (Industrial, Scientific and Medical) frequency bands [START_REF] Gutierrez | IEEE 802.15.4: A developing standard for low-power low-cost wireless personal area networks[END_REF]. The PHY layer was built upon the DSSS-OQPSK (Direct Sequence Spread Spectrum-Offset Quadrature Phase Shift Keying) modulation and provided data rates of 20 kbps and 40 kbps in the sub-GHz bands, respectively, and of 250 kbps in the 2.4 GHz band. At the MAC layer, the standard defined slotted/synchronized and unslotted/unsynchronized operation based on the CSMA/CA (Carrier Sense Multiple Access with Collision Avoidance) channel access mechanism to trade-off bandwidth, latency and energy consumption of the devices.

Thanks to its simplicity and low-cost, over the years, the IEEE 802. [START_REF] Munoz | Why Channel Hopping Makes Sense, even with IEEE802.15.4 OFDM at 2.4 GHz[END_REF].4 standard has become the basis for multiple low-power wireless communications technologies including ZigBee [START_REF] Gislason | Zigbee Wireless Networking[END_REF], ISA100.11a [START_REF]2011 Wireless Systems for Industrial Automation: Process Control and Related Applications[END_REF], WirelessHART [START_REF] Chen | WirelessHART: Real-Time Mesh Network for Industrial Automation[END_REF] and 6TiSCH [START_REF] Vilajosana | 6TiSCH: Industrial Performance for IPv6 Internet-of-Things Networks[END_REF], among others. In fact, the adoption of the IEEE 802.15.4 standard by different standardization bodies and technologies has promoted the revision of the standard (i.e., three times: in 2006, 2011 and 2015) in order to clarify the operation and to add new features to both the PHY and MAC layers. For example, the 2015 standard revision adopted the MAC layer protocols defined in the IEEE 802.15.4e-2012 [START_REF]IEEE Standard for Local and Metropolitan Area Networks-Part 15.4: Low-Rate Wireless Personal Area Networks (LR-WPANs) Amendment 1: MAC Sublayer; IEEE Std[END_REF] amendment. Among others, this amendment defined the TSCH (Time Slotted Channel Hopping), a channel access mechanism that combines TDMA (Time Division Multiple Access) and FDMA (Frequency Division Multiple Access) to support industrial requirements, including reliable packet delivery (i.e., 99.999%) in adverse conditions such as multi-path propagation and external interference.

Similarly, the IEEE 802.15.4-2015 standard revision included three new physical layers targeted to SUN (Smart Utility Network) applications, SUN-FSK, SUN-OQPSK and SUN-OFDM, as defined in the IEEE 802.15.4g-2012 [START_REF]IEEE Standard for Local and Metropolitan Area Networks-Part 15.4: Low-Rate Wireless Personal Area Networks (LR-WPANs) Amendment 3: Physical Layer (PHY) Specifications for Low-Data-Rate, Wireless, Smart Metering Utility Networks; IEEE Std[END_REF] amendment. The SUN-FSK and SUN-OQPSK modulations focus on maintaining backwards compatibility with previous standards and commercially available transceivers, whereas the SUN-OFDM focuses on adding robustness and improving spectrum efficiency at the physical layer. The benefits brought by SUN-OFDM are mainly due to the use of parallel transmissions with orthogonal sub-carriers, each transporting a small portion of the information to be transmitted using a narrow-band modulation. Such approach provides better robustness against multi-path propagation (as sub-channels can be considered flat fading, which are inherently robust to inter-symbol and inter-frame interference) and external interference (as narrow-band interference only affects a portion of the sub-channels and frequency repetition can be used to overcome its effects), as well as improving spectrum efficiency (sub-channels are optimally spaced, allowing to trade-off robustness or data-rate depending on the application requirements).

The consolidation of the IEEE 802.15.4g-2012 amendment into the IEEE 802.15.4-2015 standard, as well as the appearance of the first commercially available radio transceivers supporting it, entails a shift in the design, development and deployment of low-power wireless networks, with special interest in the industrial domain, where the propagation and interference effects have largely slowed or limited the adoption of such technologies. Taking that into account, in this paper, we focus on empirically evaluating the interference robustness of the SUN-OFDM and compare it against OQPSK-DSSS. Our goal is to provide evidence of the robustness of the different modulations, including their possible configurations and under different operating conditions, to understand the benefits and limitations when deploying such technologies. To the best of our knowledge, these results are novel and help researchers and practitioners deploy low-power wireless networks that are more robust and make an efficient use of the spectrum in real-world scenarios.

The remainder of this article is organized as follows. Section 2 provides an overview on the PHYs defined in the IEEE 802.15.4-2015 standard that are evaluated in this article. Section 3 provides a survey of the research related to the SUN-OFDM physical layer for low-power wireless networks. Section 4 presents the methodology and the setup used to conduct the experiments to evaluate the robustness of the SUN-OFDM and OQPSK-DSSS PHYs. Section 5 presents and summarizes the results obtained from the measurement campaign. Section 6 discusses the results obtained and presents a series of recommendations. Finally, Section 7 concludes this article.

IEEE 802.15.4-2015 Overview

The 2015 version of the IEEE 802.15.4 standard offers 18 different physical layers, each targeting specific applications and market segments. In this section, we present and briefly describe the two physical layers analyzed in this paper, i.e., OQPSK-DSSS and SUN-OFDM. When operating in the 780 MHz, 915 MHz, 2380 MHz and 2450 MHz bands, the PRN sequence is 32 chips long for 4 bits of data, hence providing a data rate of 250 kbps. In contrast, when operating in the 868 MHz band, the PRN sequence is 16 chips long for 4 bits of data, thus offering a data rate of 100 kbps.

As depicted in Figure 1, OQPSK-DSSS frames are composed of an SHR (Synchronization Header), PHR (PHY Header) and PSDU (PHY Service Data Unit). The SHR contains a preamble and an SFD (Start of Frame Delimiter); the PHR contains the frame length (7 bits) and a reserved bit. Hence, the maximum length of the PSDU is 127 bytes.

IEEE 802.15.4 SUN-OFDM

The SUN-OFDM (Orthogonal Frequency Division Multiplexing) physical layer was rolled into the IEEE 802.15.4-2015 version of the standard along with SUN-FSK (Frequency Shift Keying) and SUN-OQPSK (Offset Quadrature Phase Shift Keying). While FSK and OQPSK are two well-known modulation techniques that have been widely used in low-power wireless communications thanks to their simplicity, performance and low-cost, OFDM has been commonly used in other communication domains such as fixed and cellular access (e.g., xDSL, WiMAX and LTE), as well as wired and wireless LANs (e.g., PLC and Wi-Fi) due to the stringent processing, memory and energy consumption requirements.

The SUN-OFDM PHY can operate in both the sub-GHz bands (400, 700, 800 and 900 MHz) and the 2.4 GHz (2400-2483.5 MHz) with data rates from 50 kbps to 800 kbps depending on the OFDM option and MCS (Modulation and Coding Scheme) value, as summarized in Table 1.

As it can be observed in Table 1, SUN-OFDM defines four options, numbered from 1 to 4, which determine how many sub-carriers are grouped together in order to form an OFDM channel. Option 1, the largest, groups 104 sub-carriers and occupies a bandwidth of 1094 kHz with 1200 kHz of channel spacing. Option 4, the narrowest, groups 14 sub-carriers and occupies a bandwidth of 156 kHz with 200 kHz of channel spacing.

On top of that, the MCS parameter, numbered from 0 to 6, determines how each sub-carrier is modulated (available modulation for each carrier are BPSK, QPSK and 16-QAM), whether frequency repetition is applied (i.e., 4×, 2× or no frequency repetition) and the FEC (Forward Error Correction) rate applied to the input data stream for each sub-carrier (i.e., R = 1/2 or R = 3/4).

Regardless of the OFDM option and MCS value, the sub-carrier spacing and symbol rate is constant: 10416-2/3 Hz and 8-1/3 ksymbols/s. Each symbol in the OFDM physical layer is 120 µs long, although the actual symbol transmission time is divided into a BS (Base Symbol) time of 96 µs and a CP (Cyclic Prefix) time of 24 µs. For each symbol, the CP is a replica of the last 1/4 of the BS (24 µs) and is copied at the front, making the signal periodic. The long duration of an OFDM symbol and the fact that it is cyclic makes it robust against long spread time environments resulting in multi-path propagation that may cause ISI (Inter-Symbol Interference) [START_REF] Mccune | This Emperor Has No Clothes[END_REF].

As per the IEEE 802.15.4-2015 standard, SUN-OFDM frames are composed of a SHR (Synchronization Header), PHR (PHY Header) and PSDU (PHY Service Data Unit), as shown in Figure 2. The SHR is composed of a short and long preamble (STF and LTF, respectively), whereas the PHR contains a header with the receiver configuration for the PHY payload (modulation and data rate, frame length, scrambler configuration and a redundancy check). The OFDM header (SHR and PHR) is transmitted using the lowest supported MCS level for the OFDM option being used. That is, for OFDM1 and OFDM2, the header is transmitted using MCS0 (BPSK, R = 1/2, 4× repetition), for OFDM3 the header is transmitted using MCS1 (BPSK, R = 1/2, 2× repetition), and, for OFDM4, the header is transmitted using MCS2 (QPSK, R = 1/2, 2× repetition). Therefore, for any device implementing any of the OFDM options, implementation of the BPSK and QPSK is mandatory and support of 16-QAM is optional. Finally, the maximum length of the PSDU is 2047 bytes, large enough to transport a complete IPv6 packet without fragmentation.

Related Work

Despite being introduced in the IEEE 802.15.4g-2012 amendment, the SUN-OFDM PHY has not received a lot of attention from the research community to understand the potential benefits (and pitfalls) of applying this technology in low-power wireless communications for industrial applications. This is mainly due to the lack of commercially available radio transceivers that support all standard modes. In this section, we provide a summary of related work that has evaluated the performance of the PHYs proposed in the IEEE 802.15.4g-2012 amendment. The results are presented in chronological order.

In [START_REF] Sommer | Low-Power Wide-Area Networks for Industrial Sensing Applications[END_REF], the authors experimentally evaluate various LPWAN (Low-Power Wide-Area Network) technologies for industrial sensing applications, including condition monitoring. The results, which include LoRa (Long Range) and IEEE 802.15.4g (using SUN-FSK only), conclude that, with respect to IEEE 802.15.4g (SUN-FSK), LoRa provides the largest communication range (2×) at the expense of an increased energy consumption (10×).

In [START_REF] Sum | Coexistence of homogeneous and heterogeneous systems for IEEE 802.15.4g smart utility networks[END_REF], the authors study the coexistence mechanisms of homogeneous and heterogeneous IEEE 802.15.4g systems for SUN, and perform a coexistence analysis to evaluate the performance degradation of a victim system in the presence of an interferer. They show that, with a distance over 30 m, the victim and the interferer are able to coexist even without any higher layer mechanism that enforce coexistence.

In [START_REF] Liu | ah and 802[END_REF], the authors study the coexistence of IEEE 802.11 ah and IEEE 802.15.4 g networks, which provide communication ranges above 1 km, and are specifically targeted at outdoor IoT (Internet of Things) applications. Simulation results show that co-located IEEE 802.11 ah networks can severely impact the operation of IEEE 802.15.4 g networks due to the higher ED (Energy Detection) threshold and the faster back-off mechanism. Moreover, the differences in modulation scheme and frame structure limit the capability to implement automatic mechanisms to enforce cooperation. Hence, the self-coexistence mechanism needs to be enforced to mitigate the effects of interference in the network performance.

More recently, in [START_REF] Munoz | Evaluation of IEEE802.15.4g for Environmental Observations[END_REF] and [START_REF] Munoz | Overview of IEEE802.15.4g OFDM and its Applicability to Smart Building Applications[END_REF], the authors evaluate the suitability of the IEEE 802.15.4 g-2012 physical layers for environmental and smart building applications, respectively, showing that SUN-OFDM is affected by multi-path fading and external interference in a similar way as OQPSK-DSSS. Based on these results, in [START_REF] Munoz | Why Channel Hopping Makes Sense, even with IEEE802.15.4 OFDM at 2.4 GHz[END_REF], the authors conclude that the SUN-OFDM physical layer alone does not yield the robustness required for industrial applications and, thus, they recommend to add channel hopping techniques to combat its effects.

Methodology and Setup

In this section, we present the research methodology that we have used to evaluate the interference robustness of the SUN-OFDM modes and compare it with the OQPSK-DSSS mode, both defined in the IEEE 802.15.4-2015 PHYs.

Evaluation Methodology

To evaluate the interference robustness of the SUN-OFDM PHY and compare it to the OQPSK-DSSS PHY, we use the setup depicted in Figure 3. The setup consists of a transmitter, a receiver and an interferer device connected through an RF (RadioFrequency) power combiner (further described in Section 4.3).

For the SUN-OFDM modulation, we select the operating modes that provide a similar data-rate of the OQPSK-DSSS mode, 250 kbps. In particular, we select the OFDM1-MCS1, OFDM2-MCS2, OFDM3-MCS3 and OFDM4-MCS5 modes that provide a data-rate of 200 kbps but with different PHY properties (i.e., channel bandwidth, modulation, coding rate and frequency repetition) as presented in Section 2 and summarized in Table 2. For the measurement campaign, each selected modulation is used as an interferer signal, and tested against all other selected modulations acting as transmitter signals (OFDM1-MCS1, OFDM2-MCS2, OFDM3-MCS3, OFDM4-MCS5, OQPSK-DSSS). The procedure is also repeated for two different payload lengths (20 bytes and 120 bytes) in order to understand the effects of packet length on the robustness of each modulation. This is relevant as the SUN-OFDM modulation adds symbol redundancy in both time and frequency, whereas OQPSK-DSSS only adds redundancy in terms of the spreading factor gain. In addition, each base experiment is repeated twice for each transmitter and interferer device (i.e., exchanging the devices' roles). We use this approach to verify the obtained results and cancel out possible differences in the transmit power between the devices (due to the radio transceiver construction variability and/or the impedance matching of the RF circuit) that may affect the obtained results.

Overall, this gives a total of 10 base experiments, one for each interferer signal and payload length, as presented in Section 5. Each base experiment uses a particular modulation as interferer, and evaluates the robustness of all the modulations being tested in the measurement campaign, including itself. For instance, OFDM1-MCS1 is selected as interferer and tested against OFDM1-MCS1, OFDM2-MCS2, OFDM3-MCS3, OFDM4-MCS5 and OQPSK-DSSS.

To ensure that noise and external interference do not affect the results, we set the transmit power to a value that is well above the sensitivity limit of the radio transceiver for each modulation being tested, and conduct the experiments using RF coaxial cables while each board is enclosed in an individual Faraday cage. Second, when both transmitter and interferer devices use the same modulation, it is possible that the receiver synchronizes to the header transmitted by the interferer. To avoid this, the interferer device uses continuous transmit mode and starts transmitting 10 ms before the transmitter device starts sending data packets.

Base Experiment

The independent variable of each base experiment is the SIR (Signal-to-Interference Ratio), defined as the ratio between the power of the transmitter signal and the power of the interferer signal; thermal noise is not taken into account since both signals are well-above its value (P N = -107 dBm) considering the experiment conditions, i.e., ambient temperature (T = 25 • C) and signal bandwidth (B ≤ 5 MHz). In contrast, the dependent variable of each experiment is the PDR (Packet Delivery Ratio), defined as the percentage of packets that are successfully received at the receiver under the presence of the interference signal generated by the interferer device.

For all the experiments, the value of the SIR ranges from -12 dB to +6 dB, meaning that the transmitter power is between 1/16× and 4× the interferer power. We use such a wide SIR range to ensure that the PDR transitions from 100% to 0% regardless of the interferer and transmitter modulation under test. In addition, to validate the results obtained from each base experiment, the first test is conducted without interference signal (the interferer device does not transmit during that test). In that case, the PDR is expected to be 100%. This can be observed with the In f mark on the x-axis of the figures presented in Section 5.

To determine the PDR for each SIR for a given transmit modulation, the transmitter device sends 1000 frames to the receiver device. Frames are transmitted with a 5 ms inter-packet delay. The payload is composed of the {0x00, 0x01, . . . , 0x13} sequence for the 20-bytes payload and the {0x00, 0x01, . . . , 0x77} sequence for the 120-bytes payload. Each frame is completed with the FCS (Frame Check Sequence) field of the PSDU depending on the selected modulation (2 bytes for OQPSK-DSSS, 4 bytes for SUN-OFDM).

During the transmission, the interferer device injects an inteferent signal using the selected modulation for that particular base experiment. In contrast to data packets, the payload of the interference packets is composed of a 123-bytes {0x55, . . . , 0x55} sequence. That payload is transmitted continuously using the continuous transmission feature of the radio transceiver. That is, the transceiver operates in packet mode, but the packet header (SHR + PHR) is only transmitted once and the payload (PSDU + FCS) is transmitted indefinitely until the experiment is finished.

There are two conditions that need to be met for a packet to be considered successfully received. First, the FCS calculated by the receiver radio transceiver based on the received bytes has to match the FCS value attached by the transmitter device at the end of the payload. Second, the received bytes have to match the transmitted bytes depending on the packet length for that base experiment. This ensures that the PDR results are correct even in the unexpected case where the calculated FCS sequence matches the received FCS sequence despite one or multiple bit errors caused by the interferer signal.

Setup

For the transmitter, receiver and interferer devices we use the OpenMote-B [START_REF] Vilajosana | Open-Source Prototyping Platform for the Industrial IoT[END_REF][START_REF] Tuset-Peiró | OpenMote+: A Range-Agile Multi-Radio Mote[END_REF] shown in Figure 4. The OpenMote-B is equipped with a Texas Instruments CC2538 SoC (System on Chip) and a Microchip AT86RF215 radio transceiver. The CC2538 [START_REF]CC2538 Powerful Wireless Microcontroller System-On-Chip for 2[END_REF] includes an ARM Cortex-M3 micro-controller (32 MHz, 32 kB RAM, 512 kB Flash) and a radio transceiver compatible with the IEEE 802.15.4-2006 standard. The AT86RF215 [START_REF] Atmel | AT86RF215 Device Family: Sub-1GHz/2.4GHz Transceiver and I/Q Radio for IEEE[END_REF] is a dual-band (sub-GHz and 2.4 GHz) radio transceiver compatible with the IEEE 802.15.4-2015 standard, which supports all Multi-Rate PHY options defined in the IEEE 802.15.4g-2012 amendment for Smart Utility Networks (SUN). As depicted in Figure 3, the boards are connected using an Agilent 87302C RF power combiner that operates in the 0.5-26.5 GHz band and provides an input attenuation of 3 dB for the input channels towards the output channel, and a return loss of 24 dB. The output of the RF power combiner is further attenuated using a Minicircuit 30 dB RF attenuator to ensure that the received signal at the receiver device is within the receive power limits of the AT86RF215 radio transceiver (-5 dBm according to the data-sheet).

To coordinate the actions between the different devices, a computer running Ubuntu 18.04 LTS is used. The computer is connected to the OpenMote-B boards over USB, and executes a Python script that orchestrates an experiment. For each board, the script uploads the radio configuration to be used (i.e., modulation type, transmit power and packet length, among others) and starts transmission/reception. The OpenMote-B boards execute a custom firmware that receives commands over UART (Universal Asynchronous Receiver Transmitter), execute the action commanded (i.e., transmit a packet, start receiving, etc.) and return the result (i.e., packet successfully received or not).

Radio Calibration

The PDR is evaluated with respect to SIR between the transmit power of the data and the interferer signals. According to the AT86RF215 radio transceiver datasheet (specifically Figure 11-2), there is a 6 dB offset between the value of the transmit power configuration register (RFn_PAX.TXPWR) and the actual transmit power of the radio transceiver depending on the selected modulation (OQPSK-DSSS and SUN-OFDM).

Such difference in transmit power between different modulations can have an impact on the obtained results. For instance, an uncontrolled higher transmit power of the data signal results in a better PDR result for that particular modulation. Similarly, an uncontrolled lower transmit power of the interferer signal also results in a better PDR for that particular modulation. To validate the offset and obtain the configuration register values that ensure the same transmit power for both modulations, we calibrate using a Rigol DSA-815 spectrum analyzer as the Test Equipment (TE), and an OpenMote-B as the Device Under Test (DUT).

The DUT is connected to TE using an RF cable and the radio calibration procedure is performed as follows. For each modulation, the DUT is configured to transmit with a known power configuration register and the TE is configured to measure the power in the band taking into consideration the parameters of the modulation under test (i.e., center frequency, occupied bandwidth and span). The procedure is repeated for all the values of the power configuration register (from 0 to 30 with a 3-unit step) to obtain the relation between those values and the actual transmit powers that are generated by the radio transceiver, as shown in Table 3. Overall, results are in accordance with the data provided in the datasheet and allow for empirically determining the transmit power configuration register values for the OQPSK-DSSS and the SUN-OFDM modulations. In particular, we have decided to use a transmit power between -9 dBm and +9 dBm, as these are the values that are common to both modulations. We then define the default transmit power of +3 dBm, and let the interferer power range from -9 dBm to +9 dBm, corresponding to the SIR between -12 dB and +6 dB described earlier.

Results

Results obtained using the research methodology and the experiment setup described in the previous section are presented for each interferer modulation (OFDM1-MCS1, OFDM2-MCS2, OFDM3-MCS3, OFDM4-MCS5 and OQPSK-DSSS) and packet length (20 bytes and 120 bytes) in Figures 56789, respectively. Table 4 summarizes the required SIR (dB) to ensure PDR > 80% for each modulation and packet length. For example, if we consider an interfering signal modulated using OFDM1-MCS1, we can observe that, for a 20 bytes PSDU, the OFDM1-MCS1, OFDM2-MCS2 and OFDM-MCS3 physical layers perform similarly, requiring SIR > 1 dB for PDR > 80%. OFDM4-MCS5 requires SIR > 5 dB to provide a PDR > 80%. In contrast, for a 120 B PSDU, OFDM1-MCS1 requires an SIR > 2 dB, OFDM2-MCS2 and OFDM3-MCS3 require SIR > 4 dB, and OFDM4-MCS5 requires an SIR > 7 dB. Finally, for a 20 byte and 120 byte PSDU, OQPSK-DSSS requires an SIR > 8 dB and an SIR > 12 dB for PDR > 80%, respectively.

These results show that OQPSK-DSSS requires 6 dB higher SIR to achieve PDR > 80% when compared to OFDM1-MCS1 under the same interference. Considering that OQPSK-DSSS uses a 5 MHz channel bandwidth while OFDM1-MCS1 uses 1.2 MHz channel bandwidth, we can derive that OFDM provides increased spectral efficiency and robustness. Similar results can be derived for other combinations, as presented in Table 4.

Interestingly, considering an interfering signal modulated using OQPSK-DSSS, if we consider a system using OFDM1-MCS1 and we compare it to the same system using OQPSK-DSSS, we can observe that OFDM1-MCS1 can still operate with PDR>80% even if the interference level is 1 dB above the signal level. This is particularly interesting because OQPSK-DSSS is widely used.

Discussion and Recommendations

This section discusses the results outlined in the previous section and presents recommendations to researchers and practitioners, serving as a tool to understand the behavior of each particular modulation under interference conditions, and motivating the use of the SUN-OFDM for deploying low-power wireless systems in industrial scenarios.

Discussion

In the following, we discuss the results presented in Table 4. First, considering OFDM1-MCS1, we observe that a reduction in the bandwidth of the interference signal (i.e., going from OFDM2-MCS2 to OFDM4-MCS5 interference) requires a 2 dB SIR increase to provide a PDR > 80%. This can be attributed to the fact that the reduction in the bandwidth causes an increase in the PSD (Power Spectral Density) of the interference (i.e., a 3 dB increase each time the bandwidth is reduced by half) meaning that the probability of a symbol being corrupted increases.

Second, the SIR required for OFDM2-MCS2 and OFDM3-MCS3 is equivalent to OFDM1-MCS1 and OFDM2-MCS2 regardless of packet size (2-4 dB and 5-6 dB, resp.). However, the effect of OFDM3-MCS3 interference causes a 3 dB SIR increase to the OFDM3-MCS3 signal (i.e., 7-8 dB) to maintain PDR > 80%, whereas the OFDM2-MCS2 signal remains unaffected (5-6 dB). Such results can be attributed to the fact that, despite both OFDM2-MCS2 and OFDM3-MCS3 using the same modulation (OQPSK with coding rate R = 1/2), the former takes advantage of the 2x frequency repetition providing an additional protection of 3 dB. The result is independent of packet length, which confirms the importance of using such protection mechanisms at the physical layer.

Third, the SIR required for OFDM4-MCS5 to maintain a PDR > 80% is higher compared to the other SUN-OFDM modulations and increases as the bandwidth of the interferer is reduced (going from OFDM1-MCS1 to OFDM4-MCS5 interference). This is an expected result, as the PSD of the interference increases by 3 dB every time the bandwidth is reduced by two, and taking into account that OFDM4-MCS5 uses an aggressive modulation (16-QAM) in combination with a coding rate R = 1/2, but does not employ time or frequency symbol repetition, leading to a higher BER (Bit Error Rate) in the presence of interference.

Fourth, the SIR required for the OQPSK-DSSS modulation remains constant (8-12 dB depending on packet length) regardless of the type of the SUN-OFDM interference and, hence, the occupied bandwidth. In contrast, OQPSK-DSSS modulation requires a smaller SIR (6-8 dB depending on packet length) when the interference is OQPSK-DSSS. This can be attributed to a combination of facts including that SUN-OFDM interference is composed of multiple pilots spread over the channel and has a higher PSD, as well as the fact that OQPSK-DSSS does not provide any additional mechanism to enhance the robustness of the transmission against interference except for the processing gain of DSSS (10 • log 10 (2 M/250 k) = 9 dB).

Fifth, SUN-OFDM modulations are robust against OQPSK-DSSS interference, requiring negative SIR values (SIR < 0 dB) to maintain a PDR > 80%. This is an expected result that can be attributed to the fact that SUN-OFDM modulation is a combination of narrowband modulation, whereas the OQPSK-DSSS is inherently wideband, i.e., it has a very low PSD. In fact, the results show that OFDM2-MCS2 and OFDM3-MCS3 require the same SIR, which is lower than OFDM1-MCS1. This can be explained given that OFDM2-MCS2 employs 2× frequency repetition, whereas OFDM3-MCS3 occupies half the bandwidth (400 kHz vs. 800 kHz, resulting in a 3 dB PSD increase).

As a numeric example of the above, for OFDM2-MCS2, the PSD for a transmit power of 0 dBm and a bandwidth of 800 kHz is -29.03 dBm/Hz. In contrast, for OFDM3-MCS3, the PSD for a transmit power of 0 dBm and a bandwidth of 400 kHz is -26.02 dBm/Hz. Finally, OQPSK-DSSS interference with a transmit power of 0 dBm and a bandwidth of 2 MHz has a PSD of -33.01 dBm/Hz. Notice that, for an SIR = 0 dB, OFDM2-MCS2 has SIR = 4 dB (-29.03 --33.01 = 3.98 dB), whereas OFDM3-MCS3 has SIR = 7 dB (-26.02 --33.01 = 6.99 dB). In conclusion, when dealing with wideband interference (here, OQPSK-DSSS), using 2× repetition provides a theoretical 3 dB advantage, but that advantage is overcome by the bandwidth reduction that provides a higher PSD.

Another interesting result comparing the performance of the SUN-OFDM and OQPSK-DSSS physical layers against interference is that the degradation in terms of PDR caused by the increment of the packet length (going from 20 bytes to 120 bytes) is not equal for both modulation types. For SUN-OFDM, the SIR increase to maintain a PDR > 80% is bounded to 2 dB, whereas, for OQPSK-DSSS, the SIR increase is larger than 3 dB. This is thanks to time and frequency diversity, which allows for recovering random errors caused by multi-path propagation and external interference.

The SIR spread between operating in ideal conditions (PDR > 80%) and degraded conditions (PDR < 20%) for all SUN-OFDM modulations requires SIR = 3 dB regardless of the packet length. In contrast, the SIR spread between operating in ideal conditions and degraded conditions for OQPSK-DSSS depends on packet size and interference type. When dealing with SUN-OFDM interference, transitions require SIR = 2 dB for 20-byte packets, and SIR = 5 dB for 120-byte packets. In contrast, when dealing with OQPSK-DSSS interference, the transition requires SIR = 2 dB regardless of packet length.

Comparing OFDM1-MCS1 to OQPSK-DSSS, we observe that, for a PDR > 80%, it provides an advantage between 5-10 dB, depending on interference type and packet length. In particular, it provides an advantage of 5 dB for OFDM3-MCS3 interference with packet length of 20 bytes, and an advantage of 10 dB for OFDM1-MCS1 interference with packet length of 120 bytes. This is in contrast with the fact that OFDM1-MCS1 uses a channel separation of 1.2 MHz, whereas OQPSK-DSSS uses a channel separation of 5 MHz. That is, the spectral efficiency of OFDM1-MCS1 is 0.166 bits/Hz (or 200 kbps/1200 kHz), whereas the spectral efficiency of OQPSK-DSSS is 0.05 bits/Hz (or 250 kbps/5000 kHz). Hence, OFDM1-MCS1 provides an increased robustness level while offering a higher spectral efficiency that enables having denser deployments (a 333% capacity increase).

From these results, we can observe that the SIR required to provide PDR > 80% for OQPSK-DSSS largely depends on the packet length (4 dB difference). In contrast, the SIR required to provide a PDR > 80% for the robust SUN-OFDM modulations remains constant (<1 dB) regardless of the packet length and the interference type. This is owing to the fact that OQPSK-DSSS does not use any physical layer mechanism to enhance robustness except for the processing gain provided by DSSS. Hence, the error probability increases as the packet length is increased. For SUN-OFDM-based modulations, time and frequency symbol repetition reduces the probability of having an erroneous bit.

Recommendations

Based on the results and the discussion presented above, we provide the following insights and recommendations to researchers and practitioners deploying low-power wireless communication systems using the SUN-OFDM physical layer in real-world environments:

1.

Thanks to the small effect of packet length in the PDR with respect to the SIR, SUN-OFDM allows for using larger packets (i.e., packet bundling) to increase the transmission efficiency (i.e., more effective data with the same packet headers) without sacrificing robustness. In fact, SUN-OFDM allows payloads of up to 2047 bytes, effectively allowing to transmit full IPv6 packets without fragmentation or allowing to group up to sixteen 127-bytes frames in a single 2047-bytes frame.

2.

Despite the fact that SUN-OFDM transceivers consume a higher amount of energy compared to state-of-the-art IEEE 802.15.4 transceivers due to the additional circuitry required to operate (scrambler, convolutional encoder, puncturer, interleaver, Viterbi decoder), the higher level of robustness against interference provided by SUN-OFDM allows for using higher data rates (up to 800 kbps) to reduce the average energy consumption of the transmitter and the receiver devices.

3.

As the preamble of a SUN-OFDM packet is transmitted using the lowest MCS option of the current configuration, and includes information regarding the MCS option used to transmit the packet payload, this allows the transmitter to switch between different MCS options of the same SUN-OFDM configuration without any changes in the receiver configuration. It is hence possible for the transmitter to use an aggressive modulation for an initial packet transmission, and use a more robust modulation when re-transmitting. Similarly, acknowledgement frames can be transmitted using the most robust modulation to increase the probability they are received. 4.

The use of SUN-OFDM for deployments with a high device density and/or high interference levels is advisable, as it provides higher spectral efficiency, while maintaining a similar level of robustness against interference with respect to OQPSK-DSSS. If interference is of concern, choosing OFDM1-MCS1 over OQPSK-DSSS translates into a 4x capacity increase while providing an average advantage of 9 dB against the same interference. In contrast, if interference is not a concern, choosing OFDM4-MCS5 offers a 26x capacity increase, while maintaining a similar level of protection against the same type of interference.

Conclusions

This article evaluates the interference robustness of the OQPSK-DSSS and the SUN-OFDM physical layers defined in the IEEE 802.15.4-2015 standard. Interfering conditions are generated in a controlled setup to evaluate the SIR required by each modulation to achieve PDR > 80%. Compared to OQPSK-DSSS, results show that SUN-OFDM provides at least 6 dB additional protection regardless of interference type and packet length. In addition, SUN-OFDM only occupies 1.2 MHz bandwidth, whereas OQPSK-DSSS occupies 5 MHz. This results in a higher spectral efficiency that allows one to have denser deployments or to trade bandwidth efficiency and interference robustness depending on the application requirements. Overall, the presented results become a useful tool to understand the behavior of each particular modulation under interference conditions, and motivates the use of the SUN-OFDM physical layer to deploy low-power wireless systems in industrial scenarios.

2. 1 .

 1 IEEE 802.15.4-2015 OQPSK-DSSS OQPSK-DSSS was introduced in the original IEEE 802.15.4 standard in 2003 and it uses a 16-ary quasi-orthogonal modulation where each data symbol represents 4 bits of information. Therefore, there are 16 possible symbols and each of them is represented by a PRNG (Pseudo-Random Noise Generator) chip sequence that is almost orthogonal.

Figure 1 .

 1 Figure 1. IEEE 802.15.4-2015 OQPSK-DSSS frame format.

Figure 3 .

 3 Figure 3. Evaluation setup. Note that the grey box around the transmitter, interferer and receiver devices represents an RF shielding enclosure used to ensure that communication between devices can only occur through the RF coaxial cables.

Figure 4 .

 4 Figure 4. OpenMote-B board. The CC2538 (MCU) and the AT86RF215 (radio transceiver) are interconnected using the SPI bus, whereas the CC2538 (MCU) is connected to the computer using the USB-UART bridge (FTDI FT2232).

Table 4 .Figure 5 .Figure 6 .Figure 7 .Figure 8 .Figure 9 .

 456789 Figure 5. OFDM1-MCS1 interference results.

Table 1 .

 1 SUN-OFDM parameters.

	Type	Mode Modulation	Coding Rate	Frequency Repetition	Channel/Nominal Bandwidth (kHz)	Total/Data/Pilot Tones	Effective Datarate (kbps)
		MCS0	BPSK	1/2	4x			100
	OFDM1	MCS1	BPSK	1/2	2x	1200 / 1094	104/96/8	200
		MCS2	OQPSK	1/2	2x			400
		MCS3	OQPSK	1/2	0x			800
		MCS0	BPSK	1/2	4x			50
		MCS1	BPSK	1/2	2x			100
	OFDM2	MCS2	OQPSK	1/2	2x	800 / 552	52/48/4	200
		MCS3	OQPSK	1/2	0x			400
		MCS4	OQPSK	3/4	0x			600
		MCS5	16-QAM	1/2	0x			800
		MCS1	BPSK	1/2	2x			50
		MCS2	OQPSK	1/2	2x			100
		MCS3	OQPSK	1/2	0x	400 / 281	26/24/2	200
	OFDM3	MCS4	OQPSK	3/4	0x			300
		MCS5	16-QAM	1/2	0x			400
		MCS6	16-QAM	3/4	0x			600
		MCS2	OQPSK	1/2	2x			50
	OFDM4	MCS3	OQPSK	1/2	0x			100
		MCS4	OQPSK	3/4	0x	200 / 156	14/12/2	150
		MCS5	16-QAM	1/2	0x			200
		MCS6	16-QAM	3/4	0x			300

Figure 2. IEEE 802.15.4-2015 SUN-OFDM frame format.

Table 2 .

 2 IEEE 802.15.4-2015 modulations that have been selected in this study to evaluate their robustness against interference.

	Name	Mode Modulation	Channel Coding	Frequency Repetition	Receiver (dBm) Sensitivity	Effective (kbps) Data-Rate	Channel (kHz) Bandwidth	Abbreviation
	OQPSK-DSSS	N/A	OQPSK	N/A	N/A	-103	250	5000	OQPSK-DSSS
	OFDM Option 1	MCS1	BPSK	1/2	2x	-109	200	1200	OFDM1-MCS1
	OFDM Option 2	MCS2	QPSK	1/2	2x	-108	200	800	OFDM2-MCS2
	OFDM Option 3	MCS3	QPSK	1/2	0x	-107	200	400	OFDM3-MCS3
	OFDM Option 4	MCS5	16-QAM	1/2	0x	-105	200	200	OFDM4-MCS5

Table 3 .

 3 Transmit power values for the OQPSK-DSSS and the SUN-OFDM modulations. Notice that the results have been rounded to the closest dB given the resolution of the DUT (Device Under Test) and the uncertainty of the TE (Test Equipment).

	Transmit Power (dBm)

Funding: This research is partially supported by Generalitat de Catalunya (SGR-60-2017 and SGR-891-2017) and the Spanish Ministry of Science, Innovation and Universities (SPOT5G <TEC2017-87456-P> and SPOTS <RTI2018-095438-A-I00>).

Conflicts of Interest:

The authors declare no conflict of interest.

Author Contributions: P.T.-P. developed the firmware/software, conducted the experiments, obtained the graphics and contributed to writing the manuscript. F.V.-G. and J.M. equally contributed to conceptualizing the experiments, validating the results and writing the manuscript. T.W., J.A.-Z., and X.V. equally contributed to the supervision of the projects and the review of the manuscript.

Abbreviations

The following abbreviations are used in this manuscript:

BPSK


domain: spi phys

text:
A Vincent-Randonnier ‡

A Ristori

V Sabelnikov

N Zettervall

& C Fureby

A Combined Experimental and Computational Study of the LAPCAT II Supersonic Combustor

Dual-mode ramjet propulsion systems are suggested for the next generation high-speed flight vehicles. Here, we combine experimental measurements of high-speed (subsonic and supersonic) combustion at different operating conditions in the LAPCAT-II dual-mode ramjet combustor with Large Eddy Simulations (LES) using finite rate chemistry models and new skeletal H 2 -air combustion chemistry. The LAPCAT II combustor consists of four sections, and experiments have been performed for wall injection of H 2 in a Ma 2.0 vitiated airflow for total pressures and temperatures of p 0 =0.40 MPa, 1414 K<T 0 <1707 K, and a fixed equivalence ratio of φ=0.15. For this p 0 the combustor is over-expanded, and the transition from supersonic to subsonic flow occurs at the start of the fourth combustor section. The flow and combustion diagnostics include measurements of p 0 and T 0 upstream of the combustor, wall-pressure profiles and Schlieren and OH* chemiluminescence imaging. The computational set-up consists of the full combustor, from the nozzle to the dump-tank. The computational model is composed of a compressible finite rate chemistry LES model, using the mixed subgrid flow model and the Partially Stirred Reactor (PaSR) combustion model, together with a new 22 step H 2 -air reaction mechanism. Qualitative as well as quantitative comparisons between experiments and simulations show reasonable agreement, but also reveal a high sensitivity of both the LES predictions and the experiments to T 0 . The LES results are further used to describe the underlying mechanisms of flow, wall-injection, mixing, self-ignition and turbulent combustion, and how these interrelated processes are modified by increasing the total temperature under otherwise identical conditions.

I. Introduction and Background

To reach hypersonic speeds from the ground for aerospace planes, space access vehicles and military aircraft or missiles, a combined-cycle engine approach is often considered needed. Two approaches have been proposed: Rocket-Based Combined-Cycle (RBCC) engines (i.e. a combination of a scramjet flow-path with an embedded rocket engine), operated in either ejector-jet, ramjet, scramjet or rocket modes, under increasing Ma numbers, [START_REF] Kanda | Conceptual Study of a Combined-Cycle Engine for an Aerospace Plane[END_REF], and Turbine-Based Combined-Cycle (TBCC) engines (a combination of a scramjet flow-path with embedded jet engines), operated in jet-engine, ramjet and scramjet modes, [START_REF] Thomas | TBCC Technical Challenge Overview[END_REF]. The most critical features of combinedcycle-enabling combustion technologies are mode transition from the low-speed propulsion system to the highspeed propulsion system, and the subsequent transition from ramjet to scramjet combustion modes. Additional challenges include transonic aero-propulsion performance, high Ma-number jet engine technology development, advanced turbine-based combined cycle integration and innovative 3D flow-path concepts.

In this study, we will consider the transition from ramjet to scramjet combustion modes. In a ramjet, the flow is subsonic as it approaches the combustor, whereas in a scramjet the flow remains supersonic through the combustor. The dual-mode scramjet bridges the gap between the ramjet and scramjet, using the same combustor American Institute of Aeronautics and Astronautics 2 for both combustion modes but operating with a thermal throat in the ramjet mode. This may theoretically enable a vehicle to operate from Ma≈3 to Ma≈8 with only minor engine modifications. At the lower limit of this envelope, the engine operates in ramjet mode. In this mode, combustion heat-release can drive the supersonic inflow to sonic conditions, using thermal choking, whereby a pre-combustion shock-train forms in the isolator. The isolator is placed upstream of the combustor to reduce the interaction between the intake and combustor flow fields, and to prevent intake unstart. The isolator shock-train consists of a series of shocks, which terminate with a normal shock that drives the flow to subsonic conditions. The pre-combustion shock-train aids flame stabilization by increasing the static pressure and temperature whilst decelerating the flow. The pre-combustion shock-train and heat-release are strongly coupled. However, as described in Heiser & Pratt, [START_REF] Heiser | Hypersonic Airbreathing Propulsion[END_REF], at speeds approaching Ma 6, pressure losses associated with the choking increase, and operational efficiency decreases. At Ma 6, the combustion heat-release can be reduced by minor flow-path modifications, or reducing the fuel massflow rate. The dual-mode scramjet then operates in the scramjet mode, in which combustion occurs at supersonic speeds. Transition from subsonic to supersonic combustion is essentially obtained by controlling the heatrelease so that thermal choking is inhibited. Once the heat-release is reduced, the flow is no longer choked and the flow through the combustor remains essentially supersonic. For supersonic combustion the main challenges are to inject, mix, ignite and burn the fuel within the short combustor residence time.

A relatively large number of experimental dual-mode scramjet combustor studies have been reported, e.g. [START_REF] Sullins | Demonstration of Mode Transition in a scramjet Combustor[END_REF][START_REF] Dessornes | Tests of the JAPHAR Dual Mode Ramjet Engine[END_REF][START_REF] Kato | Downstream Ramjet-Mode Combustion in a Dual-Mode Scramjet Engine[END_REF][START_REF] Micka | Combustion Characteristics of a Dual-Mode Scramjet Combustor with Cavity Flameholder[END_REF][START_REF] Cabell | HIFiRE Direct-Connect Rig (HDCR) Phase I Scramjet Test Results from the NASA Langley Arc-Heated Scramjet Test Facility[END_REF][START_REF] Fotia | Mechanics of Combustion Mode Transition in a Direct-Connect Ramjet-Scramjet Experiment[END_REF][START_REF] Aguilera | Scramjet to Ramjet Transition in a Dual-mode Combustor with Finguided Injection[END_REF], using direct-connect vitiated-air facilities with oxygen (O 2 ) replacement, conventional wall-pressure measurements and optical access to facilitate Schlieren and/or OH* chemiluminescence. Some of these studies focus on fundamental as aspects such as the combustion characteristics at different stages of the transition, e.g. [START_REF] Micka | Combustion Characteristics of a Dual-Mode Scramjet Combustor with Cavity Flameholder[END_REF][START_REF] Fotia | Mechanics of Combustion Mode Transition in a Direct-Connect Ramjet-Scramjet Experiment[END_REF][START_REF] Aguilera | Scramjet to Ramjet Transition in a Dual-mode Combustor with Finguided Injection[END_REF], whereas other are somewhat more applied, e.g. [START_REF] Dessornes | Tests of the JAPHAR Dual Mode Ramjet Engine[END_REF][START_REF] Cabell | HIFiRE Direct-Connect Rig (HDCR) Phase I Scramjet Test Results from the NASA Langley Arc-Heated Scramjet Test Facility[END_REF], considering models of different flight-vehicles. The general conclusion of these experimental investigations is that the transition process is characterized by the dissolution of a pre-combustion shock train in the isolator, and if the heat addition exceeds a critical value the flow will become thermally choked and the combustor will transition back to ramjet mode, or cause unstart. The specifics of these processes, and how they interact with the flow, compressibility, mixing and combustion processes, are however not well known. Reynolds Averaged Navier-Stokes (RANS) computations have been performed on different dual-mode ramjet combustors, e.g. [START_REF] Baurle | Analysis of Dual-Mode Hydrocarbon Scramjet Operation at Mach 4-6[END_REF][START_REF] Vyas | Numerical Simulation of Vitiation Effects on a Hydrogen-Fueled Dual-Mode Scramjet[END_REF][START_REF] Quinlan | A Priori Analysis of Flamelet-based Modeling for a Dual-Mode Scramjet Combustor[END_REF], using both finite rate chemistry and flamelet models. The results show strong sensitivity of the predictions to the numerical methods, grids, reaction mechanism as well as the combustion model, and particularly the turbulence model. Large Eddy Simulations (LES) have also been successfully performed on different dual-mode ramjet combustors, e.g., [START_REF] Fulton | Large-Eddy/Reynolds-Averaged Navier Stokes Simulation of a Dual-Mode Scramjet Combustor[END_REF][START_REF] Bermejo-Moreno | Wall-Modeled Large-Eddy Simulations of the HIFiRE-2 Scramjet[END_REF][START_REF] Fulton | Large-Eddy/Reynolds-Averaged Navier-Stokes Simulations of Reactive Flow in Dual-Mode Scramjet Combustor[END_REF][START_REF] Lacaze | Large Eddy Simulation of the HIFiRE Direct Connect Rig Scramjet Combustor[END_REF][START_REF] Huang | Numerical Investigation on the Ram-Scram Transition Mechanism in a Strut-based Dual-Mode Scramjet Combustor[END_REF], using a range of flamelet and finite rate chemistry approaches. Due to the unsteady nature of LES versus RANS, more accurate and useful predictions are generally obtained since the unsteady nature of the shock train in the isolator is a key feature of the dual-mode ramjet engine concept.

In this study we combine experimental investigations of supersonic combustion at different conditions in the LAPCAT-II dual-mode ramjet combustor, [START_REF] Vincent-Radonnier | Combustion of Hydrogen in Hot Air Flows within LAPCAT-II Dual Mode Ramjet Combustor at Onera-LAERTE Facility -Experimental and Numerical Investigati-on[END_REF], with finite rate chemistry Large Eddy Simulation (LES) using skeletal H 2 -air combustion chemistry. The operating conditions are chosen to be representative of non-reacting, ramjet, dual-mode ramjet and scramjet combustion, respectively. The objectives are to examine transverse mixing, self-ignition, flame stabilization and compressible turbulent combustion, and the dependence of these phenomena on T 0 at fixed values of φ at the different operating conditions. Results from experiments and LES computations will be compared, providing reciprocal validation of the methods, and combined to provide a more comprehensive understanding of the flow, mixing and combustion phenomena occurring under typical dual-mode conditions in this semi-generic combustor.

II. The ONERA LAERTE Facility and the LAPCAT-II Dual Mode Ramjet Combustor

For the dual-mode ramjet experiments the ONERA-LAERTE facility is equipped with the LAPCAT-II dualmode ramjet combustor. The facility and the combustor and its operating conditions as well as the measurement procedures have been described in detail in [START_REF] Vincent-Radonnier | Combustion of Hydrogen in Hot Air Flows within LAPCAT-II Dual Mode Ramjet Combustor at Onera-LAERTE Facility -Experimental and Numerical Investigati-on[END_REF]. A schematic of the facility and combustor sections are presented in figures 1a to 1c, and here the facility is operated in the blow-down mode with the combustor acting as a heat-sink. The reference position, x= 0.0 m, corresponds to the throat of the Mach 2.0 nozzle as noted in figure 1c. The combustor width is 40.0 mm and the inlet height is 35.4 mm. The combustor contains four successive sections: the first has a constant cross-sectional area, whereas the following sections have 1°, 3° and 1° of diverging half-angles respectively to prevent thermal choking. The combustor length is 1257 mm. Windows are placed at different locations, allowing optical access for either single-point measurements or imaging techniques.

Experiments were performed for total temperatures, T 0 , of between 1300 K and 1800 K, at equivalence ratios, φ, between 0.10 and 0.30, at a total pressure of p 0 =0.40 MPa. All in all, around 50 experimental conditions were tested for different, T 0 and φ, resulting in a range of subsonic and supersonic combustion modes and thermal choking. The inflow air-heating was performed by hydrogen air combustion, and oxygen refill. The flow in the combustor is experimentally and computationally observed to be over-expanded, and the transition from supersonic flow to subsonic flow occurs in the far downstream part of the combustor, more specifically in the third combustor section, around x≈0.75 to 0.80 m, located in the second window. 1.

The operating conditions considered in this study focus on the range of observed subsonic and supersonic combustion modes at φ≈0.15 and p 0 ≈0.40 MPa at T 0 between 1414 K and 1720 K. Table 1 list the different case operating conditions (p 0 , φ and T 0 ) and the associated inflow air-and fuel mass-flows (m air and m H2 ) and the related air inflow velocity, v in , temperature, T in , and density, ρ in , as well as the sonic jet-in-crossflow fuel temperature, T H2 , and density, ρ H2 . The flow and combustion diagnostics include measurements of p 0 and T 0 upstream of the combustor, pressure profiles along the combustor walls, Schlieren imaging (12 kHz at 1 μs exposure time), and OH* visualization (4 kHz at 4 μs exposure time) in the three windows in figure 1c. The influence of the heat-soaking combustor material is illustrated by the difference in combustion modes observed in Cases 3a and 3b with the latter case occurring at later operating times, [START_REF] Vincent-Radonnier | Combustion of Hydrogen in Hot Air Flows within LAPCAT-II Dual Mode Ramjet Combustor at Onera-LAERTE Facility -Experimental and Numerical Investigati-on[END_REF]. The combined OH* chemiluminescence and Schlieren images, figure 1d, provide information about the flow physics and flame stabilization mechanisms, and how these attributes change with operating conditions. The shock-structure and boundary layer separation are very sensitive to T 0, and appear to dominate the ignition and flame stabilization mechanisms. For low T 0 combustion occurs in the low-speed region in the third combustor section, at midway T 0 either unsteady combustion with the combustion fronts oscillating between x≈0.25 m and x≈0.45 m or thermal choking is observed, and at high T 0 shock-induced combustion is observed.

III. LES Models, Numerical Methods and Computational Set-Up

The LES model is based on implicitly-filtered transport equations for mass, momentum, energy and species mass-fractions together with thermal and caloric equations-of-state and constitutive equations, [START_REF] Menon | Computational Combustion[END_REF][START_REF] Echekki | Turbulent Combustion: Concepts, Governing Equations and Modeling Strategies[END_REF]. The thermal and caloric equations-of-state are obtained under the assumption of a mixture of thermally perfect gases using tabulated formation enthalpies and specific heats. The constitutive equations are those of a linear viscous mixture with Fickian diffusion and Fourier heat conduction. The viscosity is calculated using Sutherland's law, whereas the thermal conductivity and species diffusivities are computed from the viscosity utilizing constant Prandtl and species Schmidt numbers, respectively, [START_REF] Giacomazzi | On the Distribution of Lewis and Schmidt Numbers in Turbulent Flames[END_REF]. The unfiltered reaction rates in the filtered species mass-fraction equations results from Guldberg-Waage law of mass-action, involving the summation over all reactions, with reaction rates obtained from Arrhenius rate laws.

The unresolved transport terms, or the subgrid stress tensor and flux vectors, in the filtered transport equations are closed by the mixed model, [START_REF] Bensow | On the Justification and Extension of Mixed Models in LES[END_REF]. The filtered reaction rates are modeled using the Partially Stirred Reactor (PaSR) model, [START_REF] Fureby | LES Modeling of Combustion for Propulsion Applications[END_REF][START_REF] Sabelnikov | LES Combustion Modeling for High Re Flames using a Multi-Phase Analogy[END_REF], which is a multi-scale model based on the observation, [START_REF] Tanahashi | Coherent Fine Scale Eddies in Turbulent Premixed Flames[END_REF], that combustion often takes place in dispersed or even intermittent fine-structure regions surrounded by low reaction rates. Here, the filtered reaction rates are modeled as a weighted average of the fine-structure and surrounding reaction rates using the reacting volume fraction, γ*, as the weighting function. Subgrid mass and energy equations are solved in all LES cells for both the fine-structure and surrounding mass-fractions and temperature, using an estimate of the fine-structures residence time, τ*. In this study, τ* and γ* are modeled using the subgrid, Kolmogorov, and chemical time-scales as detailed in [START_REF] Sabelnikov | LES Combustion Modeling for High Re Flames using a Multi-Phase Analogy[END_REF]. The LES-PaSR model has been widely used in many different combustion simulations, and is validated for laboratory combustors, [START_REF] Nogenmyr | Large Eddy Simulation and Laser Diagnostic Studies on a Low Swirl Stratified Premixed Flame[END_REF][START_REF] Fedina | A Comparative Study of Flamelet and Finite Rate Chemistry LES of an Axisymmetrc Dump Combustor[END_REF], afterburners, [START_REF] Zettervall | Large Eddy Simulation (LES) of a Premixed Bluff Body Stabilized Flame using Global and Skeletal Reaction Mechanisms[END_REF], gas turbine combustors, [START_REF] Fedina | Assessment of Finite Rate Chemistry Large Eddy Simulation Combustion Models[END_REF], and scramjet combustors, [START_REF] Fureby | A Computational Study of Supersonic Combustion in Strut Injector and Hypermixer Flow Fields[END_REF][START_REF] Nordin-Bates | Understanding Scramjet Combustion using LES of the HyShot II Combustor[END_REF].

The LES-PaSR model equations are solved using a fully-explicit finite-volume code based on the Open-FOAM C++ library, [START_REF] Weller | A Tensorial Approach to CFD using Object Oriented Techniques[END_REF]. High-order monotonicity-preserving reconstruction of the convective fluxes and central differencing of the diffusive fluxes, [START_REF] Drikakis | ILES with Limiting Algorithms[END_REF], are combined with a total variation diminishing based Runge-Kutta time integration scheme to result in a second-order accurate algorithm. The chemical source terms in the species transport equations are evaluated using an operator-splitting approach together with a stiff Rosenbrock solver, [START_REF] Hairer | Solving Ordinary Differential Equations[END_REF]. The code is density based, fully compressible, and stability is imposed using compact stencils and by enforcing conservation of kinetic energy with a Courant number limitation of 0.5.

The computational set-up is shown in figure 2, and starts at the de Laval nozzle and ends in the dump tank before the exhaust water-cooling. Hex-dominant grids with ~26 and ~77 million cells, refined along the walls and in the vicinity of the injectors and the downstream plume are used. The Index of Quality, [START_REF] Celik | Index of Resolution Quality for Large Eddy Simulations[END_REF], was used to assess the sensitivity of the solution to the grid, and reveals that 87% and 93% of the kinetic energy was resolved, respectively, rendering both grids suitable for LES. The lowest values of LESIQ occur in the highspeed injector flow. Dirichlet boundary conditions are used for all variables at the inlet, and at the sonic H 2 -injectors. Moreover, at the outlet, a wave-transmissive boundary condition is used, [START_REF] Poinsot | Boundary Conditions for Direct Simulations of Compressible Viscous Flows[END_REF], given a dump-pressure of 1.0 bar, and a no-slip subgrid wall-model, [START_REF] Fureby | On Large Eddy Simula-tions of High Re-number Wall Bounded Flows[END_REF], is employed to model the near-wall flow. The grid is adapted to the wall model, and uses y + values of between 40 and 100. The measured wall temperature is used to provide an estimate of the LES wall temperature of 700 K.

IV. H 2 -Air Combustion Chemistry

The H 2 -air combustion process is here modeled using a novel H 2 -air reaction mechanism that employs the H 2 -O 2 chemical structure from [START_REF] Larsson | Skeletal Methane-Air Reaction Mechanism for Large Eddy Simulation of Turbulent Microwave-Assisted Combustion[END_REF], with three additional fuel breakdown reactions from [START_REF] O'conaire | A Comprehensive Modeling Study of Hydrogen Oxidation[END_REF][START_REF] Alekseev | The Effect of Temperature on the Adiabatic Burning Velocities of Diluted Hydrogen Flames: A Kinetic Study using an Updated Mechanism[END_REF][START_REF] Davis | An Optimized Kinetic Model of H 2 /CO Combustion[END_REF], creating a reaction mechanism called Z22, of 9 species and 22 irreversible reactions, listed in Table 2. Hereafter, all reactions are referenced with their reaction numbers in Table 2.

In the H 2 -O 2 chemistry the chain-branching reaction R4, competes with the chain-propagating reaction R12. R4 effectively creates a pool of radicals decreasing the ignition time, whereas the hydroperoxyl (HO 2 ) producing reaction R12 constrains the chain-branching nature of the chemistry, effectively increasing the ignition time. The competition between R4 and R12, and the distribution of the fast radicals O, H and OH, and slow radical HO 2 , is very temperature dependent, and produce a region of rapid ignition, (chain-branching explosion at high temperatures), a region of slow ignition (thermal explosion at low temperatures), and a connecting region. This intermediate temperature region, the so-called crossover region, is dominated by complex chemistry, and is also where many ram-, scram-and dual mode ramjet engines typically operate. Having a chemical kinetic able to reproduce the ignition behavior in this region is important for the predictability of the ignition, flame anchoring and subsequent flame-stabilization in these engines.

The reaction mechanism Z22 includes reactions important for the complete temperature spectrum, above and below the crossover region. At high temperatures the branched-chain explosion, and its associated ignition delay, can be well described using reactions R1, R4, R5, R8 and R12, [START_REF] Sánchez | Recent Advances in Understanding of Flammability Characteristics of Hydrogen[END_REF].

As the temperature and subsequently the chain-branching reactions, decreases, new chain-propagating reaction paths become rate limiting. At lower temperatures, when R12 competes favorably with R4, the HO 2 concentration increases. This enhances the importance of alternative reaction routes, mainly via reaction R16 and R20, which will increase the H 2 O 2 concentration. The main consumption route of H 2 O 2 in Z22 is through reaction R17, creating two OH radicals that will react further mainly via reaction R8, [START_REF] Sánchez | Recent Advances in Understanding of Flammability Characteristics of Hydrogen[END_REF], in turn creating a H radical. In Z22 it is essential to increase the occurrence of reaction R17 by lowering of the activation energy in order to achieve a lowered ignition delay time at and below the crossover region. The mechanism development was performed using the laminar flame speed, s u , flame temperature, T flame , and ignition delay time, τ ign , as targets. Additional effort during the mechanism development was to create a mechanism that could match the ignition delay times in the crossover region. The detailed mechanisms of Alekseev et al., [START_REF] Alekseev | The Effect of Temperature on the Adiabatic Burning Velocities of Diluted Hydrogen Flames: A Kinetic Study using an Updated Mechanism[END_REF], K30, and Jachimowski, [START_REF] Jachimowski | An Analytical Study of the Hydrogen-Air Reaction Mechanism with Application to Scramjet Combustion[END_REF], J20, the skeletal mechanism of Davidenko & Gökalp, [START_REF] Davidenko | Numerical Simulation of Hydrogen Supersonic Combustion and Validation of Computational Approach[END_REF], D7, as well as the global mechanism of Marinov et al., [START_REF] Marinov | Detailed and Global Chemical Kinetics Model for Hydrogen[END_REF], M1, are employed for comparisons in combination with experimental data, [START_REF] Hu | Experimental and Numerical Study on Laminar Burning Velocities and Flame Instabilities of Hydrogen-Air Mixtures at Elevated Pressures and Temperatures[END_REF][START_REF] Aung | Flame Stretch Interactions of Laminar Premixed Hydrogen/air Flames at Normal Temperature and Pressure[END_REF][START_REF] Kwon | Flame/Stretch Interactions of Premixed Hydrogen-Fueled Flames: Measurements and Predictions[END_REF][START_REF] Lamoureux | Laminar Flame Velocity Determination for H 2 -air-He-CO 2 Mixtures using the Spherical Bomb Method[END_REF][START_REF] Burke | Effect of Cylindrical Confinement on the Determination of Laminar Flame Speeds using Outwardly Propagating Flames[END_REF][START_REF] Pareja | Measurements of the Laminar Burning Velocity of Hydrogen-Air Premixed Flames[END_REF][53][START_REF] Hu | Shock Tube Study on Ignition Delay of Hydrogen and Evaluation of Various Kinetic Models[END_REF][START_REF] Samuelsen | Correlation of Ignition Delay with Natural Gas and IGCC type Fuels[END_REF][START_REF] Blumenthal | Experimentelle Untersuchung und Numerische Simulation der Selbstzuendung von Kraftstoff/Luft-Gemischen im Stosswellenrohr unter Beruecksichtigung stroemungsmechanischer Einfluesse[END_REF][START_REF] Craig | A Shock Tube Study of the Ignition Delay of Hydrogen-Air Mixtures near the Second Explosion Limit[END_REF][START_REF] Slack | Rate Coefficient for H+O 2 +M=HO 2 +M Evaluated From Shock Tube Measurements of Induction Times[END_REF][START_REF] Beerer | Autoignition of Hydrogen and Air Inside a Continuous Flow Reactor With Application to Lean Premixed Combustion[END_REF][START_REF] Snyder | Shock Tube Studies of Fuel-Air Ignition Characteristics[END_REF][START_REF] Wang | Ignition of Shock-Heated H 2 -Air-Stream Mixtures[END_REF], over a pressure range from about 1.0 atm to 5.8 atm.

Figures 3a, 3b and 3c compare predictions and experimental data for s u (left axis) and T flame (right axis) at 1 atm and 300 K, and τ ign at 1 atm and 4 atm, respectively. Concerning s u , Z22 is in reasonable agreement with the experimental data and the predictions from K30, J20 and M1. For T flame , all mechanisms produce similar predictions, with the largest deviations at around stoichiometric conditions. For τ ign at 1 atm, figure 3b, all mechanisms performs similarly above 1000 K, but with deviations below. The simplified mechanism, D7 and M1, neglect the H 2 O 2 and HO 2 chemistry, results in inabilities to reproduce the bending of the ignition curve within the crossover region, and with the curves for J20 and K30 predicting higher τ ign when the temperature decreases, than Z22. At 4 atm, figure 3c, the limitation in predictions of τ ign in the crossover region and below for the different mechanisms compared to Z22 is even more obvious, with either over-or underpredictions of τ ign as compared to the data. In addition, Z22 is also the only investigated mechanism able to satisfactorily reproduce the experimental data at the lowest temperatures. Significant differences in τ ign below 1000 K between the mechanisms will critically impact anchoring and stabilization of the flame within the combustor. [START_REF] Marinov | Detailed and Global Chemical Kinetics Model for Hydrogen[END_REF], (-) Z22, (-) J20, [START_REF] Jachimowski | An Analytical Study of the Hydrogen-Air Reaction Mechanism with Application to Scramjet Combustion[END_REF], (-) D7, [START_REF] Davidenko | Numerical Simulation of Hydrogen Supersonic Combustion and Validation of Computational Approach[END_REF], (-) K30, [START_REF] Alekseev | The Effect of Temperature on the Adiabatic Burning Velocities of Diluted Hydrogen Flames: A Kinetic Study using an Updated Mechanism[END_REF], and experimental data (black symbols) from [START_REF] Hu | Experimental and Numerical Study on Laminar Burning Velocities and Flame Instabilities of Hydrogen-Air Mixtures at Elevated Pressures and Temperatures[END_REF][START_REF] Aung | Flame Stretch Interactions of Laminar Premixed Hydrogen/air Flames at Normal Temperature and Pressure[END_REF][START_REF] Kwon | Flame/Stretch Interactions of Premixed Hydrogen-Fueled Flames: Measurements and Predictions[END_REF][START_REF] Lamoureux | Laminar Flame Velocity Determination for H 2 -air-He-CO 2 Mixtures using the Spherical Bomb Method[END_REF][START_REF] Burke | Effect of Cylindrical Confinement on the Determination of Laminar Flame Speeds using Outwardly Propagating Flames[END_REF][START_REF] Pareja | Measurements of the Laminar Burning Velocity of Hydrogen-Air Premixed Flames[END_REF][53][START_REF] Hu | Shock Tube Study on Ignition Delay of Hydrogen and Evaluation of Various Kinetic Models[END_REF][START_REF] Samuelsen | Correlation of Ignition Delay with Natural Gas and IGCC type Fuels[END_REF][START_REF] Blumenthal | Experimentelle Untersuchung und Numerische Simulation der Selbstzuendung von Kraftstoff/Luft-Gemischen im Stosswellenrohr unter Beruecksichtigung stroemungsmechanischer Einfluesse[END_REF][START_REF] Craig | A Shock Tube Study of the Ignition Delay of Hydrogen-Air Mixtures near the Second Explosion Limit[END_REF][START_REF] Slack | Rate Coefficient for H+O 2 +M=HO 2 +M Evaluated From Shock Tube Measurements of Induction Times[END_REF][START_REF] Beerer | Autoignition of Hydrogen and Air Inside a Continuous Flow Reactor With Application to Lean Premixed Combustion[END_REF][START_REF] Snyder | Shock Tube Studies of Fuel-Air Ignition Characteristics[END_REF][START_REF] Wang | Ignition of Shock-Heated H 2 -Air-Stream Mixtures[END_REF].

The reason for the discrepancies between the detailed mechanism predictions and the experimental data below ~1000 K is a topic under debate, with the issue of non-homogeneous conditions being one criticism of the current way of modeling τ ign at low temperatures. Investigators, [START_REF] Blumenthal | Experimentelle Untersuchung und Numerische Simulation der Selbstzuendung von Kraftstoff/Luft-Gemischen im Stosswellenrohr unter Beruecksichtigung stroemungsmechanischer Einfluesse[END_REF][START_REF] Voevodski | On the mechanism and explosion limits of hydrogen-oxygen chain self-ignition in shock waves[END_REF][START_REF] Meyer | On the Shock-Induced Ignition of Explosive Gases[END_REF], have observed two distinct ignition phenomena depending on the temperature conditions. Z22 is designed to take the possibly non-homogeneous conditions into account when using the standard model for estimating τ ign , but a secondary approach could be to include a nonhomogeneous condition into τ ign when simulating current detailed mechanisms.

V. Results and Discussion

The focus of this investigation is to qualitatively and quantitatively examine the turbulent flow, fuel-injection, mixing, self-ignition and subsequent turbulent combustion at or in the vicinity of the operating conditions listed in Table 1, characteristic of dual-mode ramjet operation. A non-reacting case is included to provide a reference for the reactive cases, and to facilitate a discussion about the turbulent flow physics and its interactions with the shock-train in the LAPCAT-II combustor.

V.A. Non-Reacting Supersonic Flow in the LAPCAT-II Combustor

Figure 4 shows a combination of experimental images and numerical simulation results from the side of the non-reacting flow (Case 0) in the LAPCAT-II combustor (from the nozzle through to the start of the dump tank). The experimental panels show Schlieren images, in original and enlarged formats, obtained around and downstream of the location of H 2 injection in the first window. These images reveal a shock-train developing along the first constant area combustor section, continuing through the remaining combustor sections whilst being weakened and modified by the interactions with the wall boundary layer, and by the diverging combustor profile. In the successive enlargements of these images, the bow-, lambda-and barrel shocks are clearly visible as are the associated wakes and plumes (when appropriate) behind these. From these images it is also evident that the wake and plume structures interacts with the wall boundary layer and the shock-train, resulting in modified wall boundary layers and distorted shock structures. The numerical simulation results show from top to bottom a superposition of the axial velocity, v x , and the vorticity, represented by iso-surfaces of the second invariant of the velocity gradient tensor, λ 2 , colored by v x , the temperature, T, the heat-release, Q, and finally a superposition of the pressure, p, with the modeled OH* photon emission rate, k OH* . The modeled OH* photon emission rate is obtained as a post-processing step based on the global reaction H+O+M=OH*+M, with k OH* being computed from the product of the resulting OH* concentration, [OH*], and the spontaneous emission rate coefficient of [OH*], with rate constants obtained from, [START_REF] Nori | Evaluation of Chemiluminescence as a Combustion Diagnostic under Varying Operating Conditions[END_REF].

The distribution of λ 2 evolve from the very thin boundary layer in the throat of the nozzle, which start to transition just downstream of the nozzle. Gradually, typical boundary layer vortical structures develop along the walls of the first constant-area combustor section. This braid of boundary layer vortical structures becomes distorted by the wakes and plumes downstream of the bow-, lambda-and barrel shocks which develop just in front of the H 2 injectors. In case of H 2 injection, a horseshoe-vortex system is also formed around the plume that sweeps downstream parallel too but outside of the plume. The resulting vortical structures develops with downstream distance from the H 2 injectors, and in the case of H 2 injection, S-shaped side arms develop over the plume that gradually transitions into Ω-shaped vortical structures and then further into longitudinal vortices. Just downstream of the 1° to 3° transition, at 0.70<x<0.80 (m), the flow separates, and low-speed zones are formed along the upper and lower walls. Separation occurs either along the upper or the lower wall, with the line of separation oscillating back and forth. Furthermore, the separation and associated low-speed zones regularly intermittently change between the upper and lower walls, resulting in an asymmetric flow. No considerable temperature increase, heat-release or modeled OH* photon emission occurs when no H 2 is injected, but with H 2 injection ignition occurs in either the upper, lower or both boundary layers in the downstream part of the combustor, the location being dependent on T 0 . The pressure, p, reveals a distinct shock-train that traverses downstream whilst being distorted and broken-up by the interactions with the wall boundary layers and the bow-lambdaand barrel shocks as well as the plume.

V.B. Subsonic and Supersonic Combustion in the LAPCAT-II Combustor

Figure 5 shows a combination of experimental images and numerical simulation results from the side of Case 1. The experimental panels show spontaneous combustion images, obtained from an ordinary camcorder, showing approximately where combustion takes place at this operating condition. As observed, combustion starts just downstream of the 1° to 3° transition, (in the second window) at 0.75<x<0.80 m, and continues further downstream. In addition, the upper and lower flame branches appear dissimilar, with the lower flame branch being noticeably larger and more intense than the upper flame branch. The upper and lower flame branches are however found to alternate from being attached to the upper and lower walls, respectively, resulting in a symmetric mean combustion image. The simulation results show from top to bottom a superposition of contours of v x , and iso-surfaces of λ 2 , colored by v x , contours of T, contours of Q, and finally a superposition of contours of p, with the modeled OH* photon emission rate.

As for Case 0 the distribution of λ 2 evolve from the very thin boundary layer in the nozzle throat that starts to transition just downstream of the nozzle. The boundary layer continues to develop along the upper and lower combustor walls until separation occurs just downstream of the 1° to 3° transition, around x=0.75 m. After H 2 injection the upper and lower boundary layers are severely distorted by the H 2 rich plumes that are aligned by S-shaped side arms that develop over the plume, gradually transition into Ω-shaped vortical structures and then further into longitudinal vortices. A horseshoe-vortex system also from around the plume that sweeps downstream parallel too but outside of the plume. The temperature, T, and heat release, Q, distributions show consistent behaviors, with a significant increase in T following the intense heat-release from the combustion that occurs in the upper and lower wall boundary layers just after separation. By analyzing the modified Takeno Flame Index (TFI), [START_REF] Lock | Liftoff characteristics of partially premixed flames under normal and microgravity conditions[END_REF], these two flame branches are found to be premixed as the injected H 2 and the vitiated air have had sufficient time to mix prior to the ignition that takes place just downstream of the separation. The pressure, p, reveals a shock-train that traverses downstream whilst being deformed and broken-up by the interactions with the boundary layers and the bow-lambda, and barrel shocks as well as by the plume. The modeled OH* photon emission rate, k OH* , correlates well with T and Q as anticipated. Figure 6 shows a combination of spontaneous combustion images and numerical simulation results from the side of Case 3a. The numerical simulation results show from top to bottom a superposition of v x , and isosurfaces of λ 2 , colored by v x , T, Q, and a superposition of p, with the modeled OH* photon emission rate. Both the numerical simulation results and the experimental combustion images reveal that combustion occurs much earlier compared to Case 1, i.e. towards the end of the first constant area combustor section, or in the beginning of the second combustor section, both within first window. The experimental combustion images suggests a rather blunt combustion front, oscillating approximately between 0.30 m<x<0.45 m, whereas the numerical simulations predicts a somewhat more gradual combustion front, oscillating approximately between 0.28 m<x<0.40 m. Moreover, the numerical simulation suggests that the two (upper and lower) flame branches are relatively loosely coupled and hence behave rather independently.

As for Cases 0 and 1 the distribution of λ 2 evolve from the very thin boundary layer in the nozzle throat that starts to transition just downstream of the nozzle. The boundary layer continues to develop until it is significantly distorted by the combustion occurring in the boundary layer as a consequence of the H 2 injection. When the H 2 in the plume and in the horseshoe vortex system ignites, the temperature rise, the viscosity increase, the vortex structures thickens, and the topology of the vortex system in the boundary layer and in the plumes change, resulting in larger and more frequently occurring Ω-shaped vortical structures and fewer S-shaped side arms. Far downstream longitudinal vortices still dominate. The temperature, T, and heat release, Q, distributions show consistent behaviors with high values of T and Q coinciding in the first two sections of the combustor after which the high values of Q decrease as the H 2 is consumed, but with maintained high values of T in the product composition. The modified TFI, [START_REF] Lock | Liftoff characteristics of partially premixed flames under normal and microgravity conditions[END_REF], suggests that non-premixed combustion dominate this case. The pressure, p, reveal a shock-train that traverses downstream whilst being deformed and broken-up by the interactions with the boundary layers and the bow-lambda, and barrel shocks as well as the plume. The modeled OH* photon emission rate, k OH* , correlate well with T and Q as anticipated. Figure 7 shows a combination of spontaneous combustion images and numerical simulation results from the side of Case 4. The numerical simulation results show from top to bottom a superposition of v x , and isosurfaces of λ 2 , colored by v x , T, Q, and a superposition of p, with the OH* photon emission rate. Both the numerical simulation results and the experimental combustion images reveal that combustion takes place even earlier: The OH* and Schlieren images indicate that combustion starts abruptly at x≈0.26 m due to shock-induced ignition, whereas the numerical simulations suggest too early combustion, driven by shock-induced ignition, with intermittent combustion occurring also in front of the injectors, beneath the bow-shocks and partially in the horseshoe vortices surrounding the H 2 rich jets. Furthermore, all numerical simulations suggest that the upper and lower flame branches alternate from being attached to the upper and lower walls, respectively, with a frequency of approximately 50 Hz.

As for Cases 0, 1 and 3a the distribution of λ 2 evolve from the very thin boundary layer in the nozzle throat that starts to transition just downstream of the nozzle. The boundary layer continues to develop until it is significantly distorted by the combustion occurring in the boundary layer as a consequence of the H 2 injection. When the H 2 in the plume and in the horseshoe vortex system ignites, the temperature rise, the viscosity increase, the vortex structures thickens, and the topology of the vortex system in the boundary layer and in the plumes change, resulting in larger and more frequently occurring Ω-shaped vortical structures and fewer Sshaped side arms. Far downstream longitudinal vortices still dominate. The temperature, T, and heat release, Q, distributions show consistent behaviors with high values of T and Q coinciding in the first two sections of the combustor after which the high values of Q decrease as the H 2 is consumed, but with maintained high values of T in the product composition. The modified TFI, [START_REF] Lock | Liftoff characteristics of partially premixed flames under normal and microgravity conditions[END_REF], suggests that non-premixed combustion dominate this case. The pressure, p, reveal a shock-train that traverses downstream whilst being deformed and broken-up by the interactions with the boundary layers and the bow-lambda, and barrel shocks as well as the plume. The estimated OH* photon emission rate, k OH* , correlate well with T and Q as anticipated. To further elucidate the complex flow physics we next examine the perspective renderings of Cases 1, 3a and 4 in figure 8. These illustrate the flow in terms of iso-surfaces of the second invariant of the velocity-gradient tensor, λ 2 , colored by the temperature, T, filled contours of T, and semi-transparent iso-surfaces of the pressure, p. For all cases, the boundary layer flow structures (longitudinal and hairpin vortices, and streaks) leading up to the injectors are similar, after which significant differences start to appear depending on T 0 . All cases also share the physics associated with the H 2 -rich plumes behind the bow-and lambda-shocks developing over the injectors. The plumes consists of a counter-rotating vortex pair along the average trajectory of each plume, starting at the leading edges of the jet shear-layers, and jet shear-layer vortices enfolding the jets, developing from Kelvin-Helmholtz instabilities in the jet-shear layers. Near the injectors, the jet shear-layer vortices typically form S-shaped side vortex arms and rollers, gradually developing Ω-shaped vortex loops, and later longitudinal vortices. A horseshoe vortex develops in the region between the bow-and lambda shocks as a result of the flow stagnation and boundary-layer separation. Depending on the jet-to-freestream momentum ratio, J, some H 2 may be ingested into these horseshoe vortex systems that in turn merge with the corner vortices to form an complex vortex system developing parallel to the H 2 -plumes. Depending on T 0 and the resulting difference in where combustion occurs, the flow and the vortex systems vary as the density, viscosity and baroclinic torque are influenced by the exothermicity and volumetric expansion. For example, the vortical structures of Cases 3a and 4 are much thicker than those of Case 1, resulting in different mixing and turbulence production. As observed in figures 4 to 7, different combustion behaviors occur depending primarily on T 0 . This is due primarily to the different ignition and flame stabilization mechanisms dominating the different cases. For Case 1 combustion occur just after separation, downstream of the 1° to 3° transition. This is due to that the ignition delay time, τ ign , is longer than the time it takes for the flow to traverse the two first combustor sections, i.e. τ flow ≈ℓ comb /v. For Case 3a combustion occur earlier, at the end of the first constant area combustor section, or in the beginning of the second combustor section. The mechanisms for ignition are more complicated but seem to be dominated by shock-induced ignition, after which reflected shocks impinge on the plume and horseshoe vortices, creating micro-explosions that in turn ignite the neighboring mixture. For Case 4 combustion occurs even earlier and seems more intense. In the experimental images combustion is shock-induced, and follows a lambda-shock, oscillating around x≈0.26. In the numerical simulations combustion is also shock-induced, but occurs much earlier, at around x=0.22 m. Here, the shock-train first ignites the H 2 ingested in the horseshoe vortex system which then ignites the H 2 in the plume. The H 2 in the plume is also separately ignited by the shock train further downstream, around x=0.26 m. This difference may be related to inconsistencies in the reaction mechanism, inconsistencies in the estimated wall temperatures used in the numerical simulations, or to some yet unknown factor.

V.C. Comparison of Wall-pressure and 1D Metrics in the LAPCAT-II Combustor

Figure 9a and 9b show profiles of the wall-pressure, p w , from the experiments and the numerical simulations, and cross-sectional averaged profiles of the Mach number, Ma, normalized heat-release, Q/Q max , and streamthrust, s/s nozzle , in which s=p+ 1 2 ρv x 2 . Regarding p w in figure 9a we notice that the numerical simulations generally capture the trends of the experiments well, but lack somewhat in detail. For Case 0 good agreement between simulation results and experimental data is observed. For Case 1 p w increases slightly too early, suggesting too early combustion, possibly due to premature flow separation in the third combustor section. For Cases 3a and 4 both numerical simulations and experiments reveal a considerable increase in p w due to the volumetric expansion from the exothermicity. For Case 4a both the experiments and numerical simulations show a peak in p w at x≈0.26. While the experimental p w profiles are nearly constant along the second combustor section, the p w profiles from the numerical simulations decrease somewhat along the second combustor section. This difference may be explained by a small step in the combustor geometry at x≈0.60 m not included in the computational model. Moreover, the pressure recovery for x>0.80 m is reasonably well captured by all numerical simulations. Finally, comparison between measured and predicted T 0 and p 0 at x≈0.10 m shows excellent agreement for all cases indicating that the approach flow is well captured, and that the discrepancies between the experimental data and the numerical simulations are due to modeling deficiencies. For the cross-sectional averaged profiles in figure 6b we find that Q/Q max occur in different locations for the different cases: For Case 1 Q/Q max occurs in the third (subsonic) combustor section, whilst for Cases 3a and 4, Q/Q max occur in the second (supersonic) combustor section, but with different axial distributions. Ma remains almost constant until Q/Q max increases due to combustion after which Ma gradually increase for Cases 3a and 4 pending the fourth combustor section is reached, after which Ma decreases towards Ma≈0.80. Moreover, s/s nozzle is nearly constant through the combustor for Case 1 but increases along the fourth combustor section. For Cases 3a and 4 a small increase in s/s nozzle is observed along the second and third combustor sections, after which s/s nozzle increase along the fourth combustor section.

VI. Concluding Remarks

This paper describes a combined experimental and computational study of a supersonic flow and hydrogen-air combustion in the LAPCAT-II dual mode ramjet/scramjet combustor. The combustor consists of four sections with gradually increasing cross-sectional area, and experiments and LES have been performed for total temperatures of 1414 K<T 0 <1707 K at a total pressure of p 0 = 0.40 MPa and an equivalence ratio of φ=0.15. The diagnostics include reference measurements of p 0 and T 0 upstream of the combustor, wall-pressures at the combustor walls, and Schlieren and OH* chemiluminescence imaging. The LES set-up consists of the whole combustor and the LES are performed using a compressible finite-rate chemistry LES model using a novel 22 step H 2 -air reaction mechanism suitable for the low-temperature chemistry of ignition. Boundary conditions for the LES are estimated from the experiments, and this constitutes probably the weakest link of the modeling approach as the wall temperatures are poorly known and the combustor walls can be considered rough due to the use of a thermal barrier coating.

For all cases, excellent agreement between predicted and measured reference values of p 0 and T 0 is found, ascertaining mutual agreement between the experiments and LES. For this p 0 the combustor is overexpanded, and both the LES and experiments show that transition from supersonic to subsonic occur at the beginning of the fourth (and last) combustor section. By sweeping T 0 different flow and combustion states are observed: For T 0 =1414 K combustion occurs only in the separated region far downstream. For T 0 =1505 K combustion starts between the first and second combustor sections, with experiments showing an abrupt combustion front and LES a less sharp but longitudinally oscillating combustion front. For T 0 =1697 K combustion starts even earlier, with the LES predictions showing a somewhat to early, intermittent, combustion inception compared to the experimental data. Matching wall-pressure increases due to combustion are observed for the LES and the experiments. The LES and experiments both reveal a strong sensitivity of the combustor to variations in T 0 reminiscent to turbulent supersonic hydrogen-air combustion. The LES results and the OH* and Schlieren images are further utilized to describe the flow, mixing, self-ignition and turbulent combustion, and the influence of increasing T 0 .

Figure 1 .

 1 Figure 1. (a) General plan of the LAERTE facility, (b) photo of the LAPCAT-II combustor, (c) geometry of the LAPCAT-II combustor, and (d) combined OH* chemiluminescence and Schlieren images of representative combustion situations at T 0 =1697 K, cf.Table1.

Figure 2 .

 2 Figure 2. Outline and computational set-up of the LAPCAT II combustor in the ONERA LAER-TE facility including key features such as upper and lower inlet, outlet and H 2 -injection portholes.

  -exponential factor has been modified compared to the cited reference. b: Activation energy has been modified compared to the cited reference. c: Collisional coefficients H 2 :2.5 H 2 O:12.0 N 2 :1.0 O 2 :1.0. d: Collisional coefficients H 2 :1.0 H 2 O:6.5 N 2 :0.4 O 2 :0.4.

Figure 3 .

 3 Figure 3. Comparison of (a) laminar flame speeds, s u , (left axis) and adiabatic flame temperatures, T ad , (right axis) at T=300 K and p=1 atm, and ignition delay times, τ ign , at 1 atm (b) and (c) 4 atm, for H 2 -air mixtures. Legend: (-) M1,[START_REF] Marinov | Detailed and Global Chemical Kinetics Model for Hydrogen[END_REF], (-) Z22, (-) J20,[START_REF] Jachimowski | An Analytical Study of the Hydrogen-Air Reaction Mechanism with Application to Scramjet Combustion[END_REF], (-) D7,[START_REF] Davidenko | Numerical Simulation of Hydrogen Supersonic Combustion and Validation of Computational Approach[END_REF], (-) K30,[START_REF] Alekseev | The Effect of Temperature on the Adiabatic Burning Velocities of Diluted Hydrogen Flames: A Kinetic Study using an Updated Mechanism[END_REF], and experimental data (black symbols) from[START_REF] Hu | Experimental and Numerical Study on Laminar Burning Velocities and Flame Instabilities of Hydrogen-Air Mixtures at Elevated Pressures and Temperatures[END_REF][START_REF] Aung | Flame Stretch Interactions of Laminar Premixed Hydrogen/air Flames at Normal Temperature and Pressure[END_REF][START_REF] Kwon | Flame/Stretch Interactions of Premixed Hydrogen-Fueled Flames: Measurements and Predictions[END_REF][START_REF] Lamoureux | Laminar Flame Velocity Determination for H 2 -air-He-CO 2 Mixtures using the Spherical Bomb Method[END_REF][START_REF] Burke | Effect of Cylindrical Confinement on the Determination of Laminar Flame Speeds using Outwardly Propagating Flames[END_REF][START_REF] Pareja | Measurements of the Laminar Burning Velocity of Hydrogen-Air Premixed Flames[END_REF][53][START_REF] Hu | Shock Tube Study on Ignition Delay of Hydrogen and Evaluation of Various Kinetic Models[END_REF][START_REF] Samuelsen | Correlation of Ignition Delay with Natural Gas and IGCC type Fuels[END_REF][START_REF] Blumenthal | Experimentelle Untersuchung und Numerische Simulation der Selbstzuendung von Kraftstoff/Luft-Gemischen im Stosswellenrohr unter Beruecksichtigung stroemungsmechanischer Einfluesse[END_REF][START_REF] Craig | A Shock Tube Study of the Ignition Delay of Hydrogen-Air Mixtures near the Second Explosion Limit[END_REF][START_REF] Slack | Rate Coefficient for H+O 2 +M=HO 2 +M Evaluated From Shock Tube Measurements of Induction Times[END_REF][START_REF] Beerer | Autoignition of Hydrogen and Air Inside a Continuous Flow Reactor With Application to Lean Premixed Combustion[END_REF][START_REF] Snyder | Shock Tube Studies of Fuel-Air Ignition Characteristics[END_REF][START_REF] Wang | Ignition of Shock-Heated H 2 -Air-Stream Mixtures[END_REF].

Figure 4 .

 4 Figure 4. Combined experimental Schlieren image (top) together with computational images of the velocity, v x , and vorticity, λ 2 , from above and from the side, and the temperature, T, heat release, Q, and OH* photon emission rate, k OH* , for Case 0.

Figure 5 .

 5 Figure 5. Combined experimental combustion image (top) with computational images of the velocity, v x , vorticity, λ 2 , from above and from the side, and the temperature, T, heat release, Q, and OH* photon emission rate, k OH* , for Case 1.

Figure 6 .

 6 Figure 6. Combined experimental combustion image (top) with computational images of the velocity, v x , vorticity, λ 2 , from above and from the side, and the temperature, T, heat release, Q, and OH* photon emission rate, k OH* , for Case 3a.

Figure 7 .

 7 Figure 7. Combined experimental Schlieren and OH* chemiluminescence (top) with computational images of the velocity, v x , vorticity, λ 2 , from above and from the side, and the temperature, T, heat release, Q, and OH* photon emission rate, k OH* , for Case 4.

Figure 8 .

 8 Figure 8. Computational images of superimposed vorticity, temperature and pressure for Case 1 (top), Case 3a (middle) and Case 4 (bottom). In the separate insert on the top, the vorticity for Case 1 is presented as viewed from above.

Figure 9 .

 9 Figure 9. (a) Time-averaged wall-pressures, 〈p w 〉, along the lower combustor wall and (b) crosssecti-onally averaged Mach number, Ma, and normalized heat-release, Q/Q max , and streamthrust, s/s nozzle . Legend: (!), (!), (") and (") experimental data for Cases 1, 3a and 4, respectively, and LES predictions for (-), (-), (-) and (-) Cases 0, 1, 3a and 4, respectively, on the 26 million cell grid. In (b) solid lines denote Ma, dotted lines denote Q/Q max and dashed lines denote s/s nozzle .

Table 1 .

 1 Characteristic properties of the LAPCAT-II combustor simulations.

	Case p 0 [Pa] T 0 [K] m air [kg/s] m H2 [g/s] φ v in [m/s] T in [K] ρ in [kg/m 3 ] ρ H2 [kg/m 3 ] T H2 [K	Combustion
	0 397740 1414 0.2931	0	0	686 1199	0.614	0.176	294	Non-reacting
	1 397740 1414 0.2931	1.53 0.15 686 1199	0.614	0.176	294	subsonic
	3a 401550 1505 0.2931	1.47 0.15 707 1276	0.583	0.173	297 unsteady supersonic
	3b 400900 1506 0.2931	1.49 0.15 708 1277	0.582	0.173	299	thermal choking
	4 410220 1697 0.2931	1.40 0.15 751 1439	0.525	0.165	306	shock-induced
	5 402550 1707 0.2931	1.37 0.15 754 1448	0.515	0.163	304	shock-induced

Table 2 .

 2 The Z22 reaction mechanism (k=A•T n •exp(-E a /RT), units: s, mole, cm 3 , cal, K).

	# Reaction	A	N	E a	Ref.
	1 H 2 + O 2 → H + HO 2	7.40E+05 2.43 53500 [41]
	2 H 2 + M → H + H + M	4.57E+19 -1.4 105100 [40], c
	3 HO 2 + H 2 → H 2 O 2 + H	3.00E+06 2	21000 [42]
	4 H + O 2 → OH + O	2.45E+14 0	16800 [39], a
	5 OH + O → H + O 2	1.20E+13 0	690	[39]
	6 O + H 2 → OH + H	1.80E+10 1	8826	[39]
	7 OH + H → O + H 2	8.00E+09 1	6760	[39]
	8 H 2 + OH → H 2 O + H	1.17E+09 1.3 3626	[39]
	9 H 2 O + H → H 2 + OH	5.09E+09 1.3 18588 [39]
	10 OH + OH → O + H 2 O	6.00E+08 1.3 0	[39]
	11 O + H 2 O → OH + OH	5.90E+09 1.3 17029 [39]
	12 H + O 2 + M → HO 2 + M	1.80E+18 -0.8 0	[39], a, d
	13 H + HO 2 → OH + OH	1.50E+14 0	1004	[39]
	14 H + HO 2 → H 2 + O 2	2.50E+13 0	700	[39]
	15 OH + HO 2 → H 2 O + O 2	2.00E+13 0	1000	[39]
	16 HO 2 + HO 2 → H 2 O 2 + O 2	8.00E+13 0	0	[39]
	17 H 2 O 2 + M → OH + OH + M 1.30E+17 0	34500 [39], b
	18 OH + OH + M → H 2 O 2 + M 9.86E+14 0	-5070 [39]
	19 H 2 O 2 + OH → H 2 O + HO 2 1.00E+13 0	1800	[39]
	20 H 2 O + HO 2 → H 2 O 2 + OH 2.86E+13 0	32790 [39]
	21 OH + H + M → H 2 O + M	2.20E+22 -2 0	[39]

Acknowledgement

The authors acknowledge the support of ONERA and FOI, respectively; VS was also supported by the Grant of the Ministry of Education and Science of the Russian Federation (Contract No. 14.G39.31.0001 of 13.02.2017).