Methane Absorbance Measurements at Pressure/Temperature Conditions Associated With Hypersonic Flight

American Institute of Aeronautics and Astronautics

1

Methane Absorbance Measurements at

Pressure/Temperature Conditions Associated With

Hypersonic Flight

Daanish Maqbool1 and Christopher Cadou

2

University of Maryland, College Park, MD, 20742

A facility constructed for simulating high pressure and temperature fuel flows in

endothermic cooling channels for hypersonic air-breathing engine components has been

used to investigate methane absorption at elevated temperature and pressure. Absorption by

two rovibrational lines around 1654 was measured at pressures ranging from 1 to 15 atm

and at 300 and 700K. The results show that measured integrated absorbance differs

substantially from HITRAN predictions and can lead to errors of more than 40% in

predicted concentration. This is probably because HITRAN relies almost entirely on

spectroscopic data acquired at atmospheric temperature and pressure but more detailed

investigations are required to confirm these findings and to better quantify the discrepancy.

Nomenclature

C = concentration

D = diffusion coefficient

E = error

= molar absorptivity

H = height of channel

I = Intensity

k = absorption coefficient

L = length scale

P = pressure

Pe = Peclet number

Re = Reynolds number

= density

Sc = Schmidt number

T = temperature/transmittance

u = velocity

= viscosity

= optical frequency/wavenumber

x = length

I. Introduction

ne thermal protection strategy being considered for hypersonic engines is active cooling of internal engine

components by endothermically decomposing fuel in millimeter-scale passages machined into the

components1. An important additional benefit of this approach is that the decomposition products typically have

lower ignition delay and reaction times making it easier to complete combustion in the high speed engine

environment2. However, the thermodynamics of the gas-phase cracking process favors soot-producing pathways that

would quickly clog the small cooling passages2,3

and cause a catastrophic loss of cooling performance. An

interdisciplinary team of researchers from the University of Virginia, North Carolina State University, and the

1Research Assistant, Department of Aerospace Engineering, Univ. of Maryland, College Park, MD 20742

2Associate Professor, Department of Aerospace Engineering, Univ. of Maryland, College Park, MD 20742,

Associate Fellow of AIAA

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53rd AIAA Aerospace Sciences Meeting 5-9 January 2015, Kissimmee, Florida

AIAA 2015-1156

Copyright 2015 by Daanish Maqbool and Christopher Cadou. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

AIAA SciTech


2

University of Maryland is pursuing a solution to this problem where mixed metal acid catalysts are used to promote

non-soot producing endothermic decomposition pathways. Part of this effort involves making non-intrusive

measurements of fuel and decomposition product concentration profiles along the length of cooling micro-channels

at temperatures and pressures that are representative of injection conditions in hypersonic engines (up to 50 atm and

1100 K). Chemical kinetic analyses indicate that knowledge of the concentrations of stable species like CH4, C2H2,

C2H4, and C2H6, and radical species like CH3 and C3H3 will be especially important for understanding the

decomposition process. However, making non-intrusive measurements of these species is challenging not only

because of the small size of the cooling passages but because of the lack of spectroscopic data at the appropriate

temperatures and pressures.

This paper describes the development of a facility for investigating the endothermic decomposition of liquid

hydrocarbon fuel surrogates like dodecane (C12H26) in micro-channels and its first use to acquire some of the basic

absorption data needed to make non-intrusive measurements of species concentrations in microchannels at

conditions that are representative of the hypersonic environment. The focus of the latter effort is on measuring

absorption line strength of the R(3) line in the 23 manifold of methane (~1654 nm) at high temperature and pressure. This line was selected not only for its relevance to the endothermic decomposition problem but also for its

usefulness in the development of non-intrusive equivalence ratio sensors for gas turbine combustors that are accurate

at realistic combustor temperatures and pressures.

II. Experiment Design

A. Determination of representative hypersonic conditions

Calculations were performed to identify fuel injector conditions that are representative of flight between Mach 3 and

7 at altitudes between 30,000 and 100,000 feet. Atmospheric conditions as a function of altitude are determined

using the International Standard Atmosphere (ISA). Static pressure and temperature of the air entering the

combustor are plotted in Fig. 1 (log scale) for incoming Mach numbers of 0.3 and Mach 1.5. The dashed lines show

the boundary beyond which dodecane (i.e. the fuel surrogate of interest here) is supercritical. The green box shows

the region accessible in the experimental facility.

Fig. 1: Representative hypersonic combustor inlet conditions.

103

10-1

100

101

102

103

Temperature (K)

Pre

ssure

(atm

)

Mach 7 at

30,000 ft

Mach 3 at

30,000 ft

Mach 3 at

100,000 ft

Super-

-critical

Mach 7 at

100,000 ft

Mcombustor

= 0.3

Mcombustor

= 1.5

Supercritical

Experiment Test Conditions

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B. Determination of flow rates

Fig. 2 is a schematic illustration of the lower half of the flow in the simulated cooling channel. A fuel surrogate

in this case dodecane heavily diluted with N2 to avoid coking upstream enters from the left. The wall supported

catalyst initiates decomposition to lighter species (H2, CH4, etc.) that diffuse off the surface back into the flow. The

channel has a 4 mm x 4 mm square cross-section and is 152 mm (6 inches) long. These dimensions were selected to

be consistent with what one might find in a practical endothermic cooling application and to be consistent with

similar experiments being carried out at other laboratories. The objective is to make non-intrusive measurements of

chemical composition at different axial locations in order to observe the streamwise evolution of the decomposition

process. However, it is important that the experiments span the full range of conditions that could be encountered in

the real flow.

Fig. 2: Diffusive transport in the microchannel.

The Peclet number is a convenient parameter for describing mass transport in this flow. It is defined as follows

D

uH

D

uLScPem ===

Re (Eq. 1)

where H is the cross-sectional dimension of the passage, u is the convective velocity, and D is the diffusion

coefficient of the particular species of interest. When the Peclet number is large, the time required for a molecule to

diffuse from the core flow to the wall is much larger than the time required for the molecule to be convected

downstream and the decomposition rate is said to be transport limited. Conversely, when the Peclet number is small,

the time required to diffuse to the wall is much smaller than the time to be convected downstream and the

decomposition rate is determined by the activity of the catalyst and is said to be rate limited. Since the channel

dimensions (H) and the diffusion coefficient (D) are fixed parameters of the experiment, exploring the full range of

operating conditions from transport limited to rate limited is achieved by varying the flow velocity (u).

It should be noted that determining the diffusion coefficient upon which these calculations are based is not

necessarily trivial for the supercritical conditions expected in the experiment. One could use numerical tools that

rely on molecular dynamics4 (such as CANTERA

5) or empirical correlations (such as the Wilke-Change

6, Stokes-

Einstein7, or He-Yu

7) to calculate the diffusion coefficients of the various species into N2. Unfortunately, however,

these methods give results that vary by over two orders of magnitude. This is mainly because the correlations have

been developed for specific industrial processes that are not relevant here and because CANTERA uses gas

dynamics models which are strictly valid only in the gaseous phase. In order to avoid getting bogged down in a

different problem, the approach taken here is to compute all diffusion coefficients using CANTERA in order to

ensure some measure of consistency. The results of these calculations for the diffusion of several important species

into N2 are tabulated in Table 1. These diffusion coefficients are averaged (4.85e-6 m2/sec) for the purpose of

determining the general range of u.

Wall

H2, CH4, C2H4, C6H6,

etc. diffusing upward

C-L

C12H26 diffusing

downward Catalytic Surface

Tfuel

Twall

Interrogation

Beam

Dodecane Species Boundary

Layer

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Table 1: CANTERA results for diffusion into N2.

Solute (diffusion into N2) D (m2/sec.) CANTERA

Hydrogen (H2) 1.39e-5

Methane (CH4) 4.22e-6

Ethylene (C2H4) 3.20e-6

Benzene (C6H6) 1.82e-6

Dodecane (nC12H26) 1.11e-6

The range of Peclet numbers of interest here is 0.1 to 100 and is chosen to span the range from rate-limited to

transport-limited performance. Under these conditions, the corresponding flow velocities (using Eq. 1) will range

between 0.000121 and 0.121 m/s. Assuming a 90% dilution (by volume) with N2, and given the state of the N2-fuel

mix (from CANTERA), the required mass flow rate of the fuel is between 4.33e-8 kg/sec (43.4 ug/sec) to 4.33e-5

kg/sec (43.3 mg/sec). Given the available fuel metering pump (an Eldex Laboratories Model 1LMP metering pump

that can meter between 0.002 and 2.5 mL/min. at up to 6000 psi), Peclet numbers as low as 1 should be attainable.

C. Overall Design

Fig. 3 is a sketch of the experiment layout. The test section is a rectangular channel with two sides (top and

bottom) serving as the catalyst surface, and the other two sides formed by Zinc-Selenide windows for optical access

in the IR-region. It is housed in a pressure vessel equipped with optical ports and a 3-zone tube furnace (Fig. 4). The

vessel can be pressurized up to 50 atm with Nitrogen in order to ensure that the fuel inside cannot oxidize in case the

test section leaks or breaks. The internal dimensions of the pressure vessel are 0.254 m (10 inches) in diameter and

0.6096 m (24 inches) in length.

Nitrogen from the high pressure environment enters the test section via a 1.82 m (6 foot) long tube coiled inside

the furnace as shown in Fig. 5. This ensures that the Nitrogen enters the test section at the furnace temperature. A

thermocouple monitors the temperature of the N2-fuel mix before it enters the test section. The flow rate of the

Nitrogen is controlled by a choked flow orifice downstream of the test section and the fuel flow rate is set

independently by the metering pump.

The flow is probed optically at various downstream locations through the 6 inch long ZnSe windows using a

Thermo-Nicolet Nexus 870 FT-IR spectrometer with a Thorlabs BF20LSMA optic fiber. Unreacted fuel leaving the

test section is condensed out in an external shell-and-tube heat exchanger before the gas stream is exhausted to the

atmosphere.

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Fig. 3: Experiment Layout.

Fig. 4: Pressure vessel with tube furnace inside.

High Pressure

N2

Tube Furnace (up to 1100 K)

Test Section

Pressure Chamber

Pump

Water

N2

Pressure Controller

N2

Condensed Fuel

N2

Independently Set Temperature

Independently Set Fuel Flow

Rate

Independently Set System Pressure

Do not want to release vaporized fuel at 800 C and

50 atm into air

Shell and Tube heat exchanger

condenses reaction products for safe ejection

Choked Orifice Flow

Meter

Measure P, T

Fuel

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Fig. 5: Test section with heating coil for N2.

III. Spectroscopic Measurements

A. Absorption Spectroscopy

Absorption spectroscopy is a well-established technique for making non-intrusive measurements of species

concentration. The Beer-Lambert law8,9

describes the relationship between optical absorption and absorbing-species

concentration:

CdxkI

dI)(

)(

)(

0

= (Eq. 2)

In this expression, I0 is the initial light intensity, dI is the measured change in transmitted intensity, is the optical frequency (typically in cm

-1), C is the concentration in moles/m

3, dx is the differential path length, and k is a

coefficient that accounts for the variation of absorption with wavelength. Note that k may also depend on

temperature and pressure. Integrating over the optical path length L and converting natural logarithms to base 10

gives:

CLAI

dI)()(

)(

)(log

0

10

== (Eq. 3)

where A is the absorbance and is the molar absorptivity, The wavelength-integrated absorbance (

== ))( CLCLdA is the sum of the absorbance over a particular absorption feature or the entire absorbing rovibrational band. In cases where the molar absorptivity is not known directly, concentration can be

inferred from a calibration:

.ncalibratio

sample

ncalibratio

ncalibratio

sample

sample CL

L

A

AC = (Eq. 4)

B. Selection of Absorption Lines

This experiment will use absorption spectroscopy to infer concentrations of species of interest at different axial

locations in a test section. As explained in the previous section, at a given temperature and pressure, and for a given

geometry (i.e. path length), absorbance (or transmittance) is just a function of the concentration. A higher

absorbance implies a higher concentration and vice versa. Absorption lines to probe must be selected for each

species of interest. These lines should be as strong as possible (to facilitate detection) and should be free of

interference from absorption by other species in the experiment. Table 2 shows the main species involved in

dodecane cracking. Spectroscopic data for four of these species are available in HITRAN12

and their respective

linestrengths are plotted in Fig. 6. The figure shows that interference-free lines for CH4 can be sought in the region

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2700-2900 cm-1

, for C2H2 in the region 6400-6700 cm-1

, for C2H4 in the region 900-1100 cm-1

, and for C2H6 in the

narrow region 800-820 cm-1

.

Fig. 6: Linestrengths for species of interest (from HITRAN

12/SpectralCalc

29). Minimum intensity (Icut) is 1e-23

cm-1

/(mol-cm-2

).

C. Motivation for Methane and Spectroscopic Challenges

The chemical species of interest in dodecane cracking are listed in Table 2 along with references to spectroscopic

data for these molecules taken from the HITRAN 2012 database13

. The table shows that most of the data available

for these species has been acquired at temperatures and pressures that are much lower than those of interest in this

work. Other databases (GEISA, JPL Mol. Spec., etc.) are, to the authors knowledge, also intended for low-

temperature studies. This could pose a problem for the use of non-intrusive measurement techniques if the

spectroscopic parameters of these molecules (line positions, line strengths, pressure broadening coefficients, etc.) are

substantially different at the elevated pressures and temperatures of interest here. So, the first step of this research

endeavor is to establish the degree to which the spectral parameters of the various molecules of interest vary with

temperature and pressure.

Table 2: Species of interest in dodecane cracking.

Species Spectral Data

T (K) P(atm) Reference

CH4


8

high pressures and temperatures, and is accessible through the inexpensive borosilicate glass windows of the

pressure vessel.

Table 3: Previous spectroscopic investigations of methane.

D. Experiment Setup

Fig. 7 shows the experiment setup for making the measurements described in the previous section. White light

from a Thermo-Nicolet Nexus 870 FT-IR is channeled into a Thorlabs BF20LSMA optic fiber using a custom-

assembled fiber coupler using Thorlabs cage-and-tube kit components. The light exits the fiber into a Thorlabs

RC04SMA-P01 reflective collimator. The 0.66 mm (0.26 in.) diameter collimated beam passes through the pressure

vessel and furnace (which host the gas mixture to be probed) via two 0.0127 m (0.5 inch) thick Borosilicate

windows. An MCT/A* detector on the other side of the vessel receives the beam and interfaces with the

spectrometer. The resolution of the spectrometer is 0.5 cm-1

and the spectra represent the average of 600 scans.

It was determined that 600 scans were adequate to resolve the main features of interest by computing the change

in mean transmittance with the number of scans which should be set high enough that the mean transmittance is

independent of the number of scans. The mean transmittance () is defined as = , where T is the

transmittance ( = ) at a given wavenumber (), and 1 and 2 are the lower and upper limits of the wavenumber range of interest. For the test case at 700 K and 15 atm, averaging 100 scans gives =93.0929, 350 scans gives = 92.9397, and 600 scans gives =92.9326. While is not an indication of the level of random noise in the signal (because the random noise component should integrate to zero), the convergence in values indicates that 600

scans is at least sufficient to resolve physical features. Of course, higher numbers of scans are still desirable to

reduce noise, especially given the challenge of obtaining good Signal-to-Noise Ratio (SNR) in this apparatus, but

600 scans appears to represent a good compromise between accuracy and measurement time.

Author Year Wavelenngth Temperature Pressure Ref

Max Min Max Min Max Min

(nm) (nm) (K) (K) (atm) (atm)

Frankenberg 2008 1670.84 1616.81 296.15 295.65 0.123 0.888 21

Gharavi et. al. 2005 1650.98 1653.99 908 296 0.021 0.003 22

Darnton and Margolis 1973 1662.33 1659.41 300 100 1.711 0.658 23

Nagali et. al 1996 1645.57 1645.53 295 292 0.017 0.004 24

Margolis 1988 1818.18 1618.12 296.2 295.6 0.059 0.002 25

Margolis 1990 1818.18 1618.12 220 180 0.026 26

Li et. al 2011 1653.73 1653.73 578 297 1.000 1.000 20

Lackner 2003 1687.42 1683.90 296 296 0.010 1.283 27

Niederer 2011 11111.11 833.33 80 80 0.007 28

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Fig. 7: Top View of Spectroscopic Measurement Setup.

IV. Results

The upper sections of each plot in Fig 8 show percent transmittance of 6% mixtures of methane (CH4) in

nitrogen (N2) around 1654 nm at temperatures of 300 K and 700 K and at several pressures between 1 and 15 atm.

The lower section of each plot shows error computed by taking the difference between the measured transmittance

and that predicted using SpectralCalc29

and the HITRAN database12

. Fig. 9 shows corresponding absorbance at each

condition. The residual is the difference between the measured and predicted values normalized by the maximum

measured absorbance of each peak. Thus, the absorbance used for normalization in the left half of the plots

corresponds to the peak at ~6057 cm-1

and the value used for normalization in the right half of the plot corresponds

to the peak ~6057 cm-1

.

The results illustrate the competing effects of pressure and temperature. Generally speaking, raising the

temperature decreases absorbance, because it lowers the density and thus the total number of light-molecule

interactions. Conversely, raising the pressure increases the density resulting in more interactions and higher

absorbance. Pressure broadening is also apparent in all cases but is not strong enough to render individual peaks

indistinguishable for these lines under these conditions.

It is also apparent from Figs. 8 and 9 that there are differences between the measured and HITRAN-predicted

spectra that seem to increase with temperature. The importance of these differences for making non-intrusive

measurements of concentration is determined by computing the error in predicted concentration. The error is

defined as:

= 100 (Eq. 5)

where CH and CM are the concentrations computed using Eqn. 4 and the Hitran (H) and measured (M) absorbance

spectra. Since all measurements and HITRAN simulations have been performed at one path length and one

concentration, Eq. 5 reduces to:

Fiber

Coupler

Optic

Fiber

Collimator

Borosilicate

Windows

MCTA*

Detector Test Vessel Spectroscope

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= 100 1 (Eq. 6)

Fig. 10 shows percent error in predicted concentration as a function of pressure at two temperatures: 300K and

700K. To obtain respective values, the absorbance was integrated between 6046 cm-1 and 6048 cm-1 for the peak at ~6047 cm

-1, and between 6056 cm

-1 and 6058 cm

-1 for the peak at ~6057 cm

-1. While error is relatively modest at

300K (a few percent which probably of the order of the uncertainty in the measurement although this has not been

calculated yet) and remains so at pressures up to about 5 atm, it grows substantially beyond this point and errors in

predicted concentration of 30-40% are observed when using either line. The results are even worse at 700K where

the error at 5 atm is already ~30-40%. However, the high temperature results in particular expose an important

problem with the experiment which is generally low absorbance (and thus SNR) throughout. The problem was so

severe at 700K and 1 atm that the absorption features of interest disappeared and hence no comparisons between

HITRAN and experiment were possible.

V. Conclusions and Future Work

A facility has been constructed for simulating the high pressure and temperature fuel flows encountered in

miniature channels used for cooling hypersonic air-breathing engine components via endothermic fuel

decomposition. Before the facility may be used to measure chemical composition as a function of downstream

distance in the optically accessible cooling channels, it is necessary to establish the efficacy of the non-intrusive

absorption-based technique used to measure chemical composition. To this end, the absorption by two rovibrational

transitions of methane around 1654nm has been explored at two temperatures (300K and 700K) over pressures

ranging from 1 to 15 atm. These lines were selected for their additional usefulness in the development of non-

intrusive equivalence ratio sensors for gas turbines19,20

. The results show that measured integrated absorbance differs

substantially from that predicted by HITRAN and can lead to substantial errors of more than 40% in predicted

concentration. This is probably because HITRAN relies almost entirely on spectroscopic data acquired at

atmospheric temperature and pressure but a more detailed investigation is required to confirm these findings and to

better quantify the discrepancy. In particular, uncertainty levels associated with each data point in Fig. 10 need to be

determined, the range of conditions needs to be expanded (experiments 50 atm and 1100K are planned), experiments

at concentrations other than 6% need to be performed, and the SNR of the measurement system needs to be

improved. Once these steps have been taken, we will move on to C2H2, C2H4, C2H6, and other molecules relevant to

dodecane cracking.

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300 K 700 K 1

atm

5 a

tm

10

atm

15

atm

Wavenumber (cm

-1)

Wavenumber (cm

-1)

Fig. 8: Spectroscopic Measurements of Methane (Transmittance).

0

20

40

60

80

100

120%

Tra

nsm

issio

n

6040 6045 6050 6055 6060-10

0

10

-1

Err

or

0

20

40

60

80

100

120

% T

ransm

issio

n

6040 6045 6050 6055 6060

-10

0

10

-1

Err

or

Experiment

HITRAN (SPECTRA)

0

20

40

60

80

100

120

% T

ransm

issio

n

6040 6045 6050 6055 6060-10

0

10

-1

Err

or

0

20

40

60

80

100

120

% T

ransm

issio

n

6040 6045 6050 6055 6060-10

0

10

-1

Err

or

0

20

40

60

80

100

120

% T

ransm

issio

n

6040 6045 6050 6055 6060-10

0

10

-1

Err

or

0

20

40

60

80

100

120

% T

ransm

issio

n

6040 6045 6050 6055 6060-10

0

10

-1

Err

or

0

20

40

60

80

100

120

% T

ransm

issio

n

6040 6045 6050 6055 6060-505

1015

-1

Err

or

0

20

40

60

80

100

120

% T

ransm

issio

n

6040 6045 6050 6055 6060

-15-10-50

-1

Err

or

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300 K 700 K 1

atm

5 a

tm

10

atm

15

atm

Wavenumber (cm

-1)

Wavenumber (cm

-1)

Fig. 9: Spectroscopic Measurements of Methane (Absorbance).

0

0.1

0.2

0.3

0.4A

bsorb

ance

6040 6045 6050 6055 6060-40-20

02040

-1

Resid

ual (%

)

0

0.1

0.2

0.3

0.4

Absorb

ance

Experiment

HITRAN (SPECTRA)

6040 6045 6050 6055 6060-100

0

100

-1

Resid

ual (%

)0

0.1

0.2

0.3

0.4

Absorb

ance

6040 6045 6050 6055 6060-20

0

20

-1

Resid

ual (%

) 0

0.1

0.2

0.3

0.4

Absorb

ance

6040 6045 6050 6055 6060-50

0

50

-1

Resid

ual (%

)

0

0.1

0.2

0.3

0.4

Absorb

ance

6040 6045 6050 6055 6060-10

0

10

20

-1

Resid

ual (%

)

0

0.1

0.2

0.3

0.4

Absorb

ance

6040 6045 6050 6055 6060

-40-20

020

-1

Resid

ual (%

)

0

0.1

0.2

0.3

0.4

Absorb

ance

6040 6045 6050 6055 6060

0

20

40

-1

Resid

ual (%

) 0

0.1

0.2

0.3

0.4

Absorb

ance

6040 6045 6050 6055 6060

-40

-20

0

-1

Resid

ual (%

)

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Fig. 10: Percent error in predicted values of .

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0 5 10 150

10

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Pressure (atm)

7 APercentE

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Line 1 (~6047 cm -1)

Line 2 (~6057 cm -1)

300 K

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Methane Absorbance Measurements at Pressure/Temperature Conditions Associated With Hypersonic Flight

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