Experimental Methodology for Estimation of Local Heat Fluxes and Burning Rates in Steady Laminar Boundary Layer Diffusion Flames

Experiments have been performed both in a vertical configuration and a unique horizontal wind tunnel facility at the University of Maryland, shown in Figure 1. Rather than a traditional pull or closed return wind tunnel, the wind tunnel facility at the University of Maryland uses a variable speed blower to pressurize a 100 x 75 x 100 cm plenum which drives the flow of air out a duct at the opposite end. This configuration enables continuous combustion experiments as smoke is not re-circulated, the wind tunnel is not damaged or influenced by the fire and thermocouples are able to freely move throughout the sampling section. The exit duct consists of a 122 cm, 30.5 cm wide converging section connected to the plenum. To straighten the flow and reduce the incoming turbulence intensity, fine mesh screens are placed at the entrance and exit of the converging section and a 5 cm thick honeycomb with 0.3 cm holes is placed 110 cm upstream from the tunnel exit. The velocity of the flow exiting the wind tunnel is controlled by varying the speed of the fan with a pulse-width-modulation (PWM) controller and fuel samples are placed at the outlet of the tunnel, where flow velocities have been checked via the use of a hotwire anemometer.

Fuel samples at the outlet of the wind tunnel were placed on top of a load cell which continuously measures the mass-loss of the sample over time. To avoid disturbances of the wind to the load cell, the sample was elevated on a sheet of aluminum (30.5 x 61.0 cm x 1.5 mm thick) by two U-brackets and surrounded by 1.27 cm thick ceramic fiber insulation board to ensure a smooth surface around the burning sample. The top surface of the board was coated with a high temperature black matte paint with an emissivity approximately 98% to ensure a good backdrop for visually observing the flame and to seal the insulation which also contains organic binders. Because the insulation board presents a relatively blunt body to the incoming flow, placing the sample setup directly in the outlet of the wind tunnel resulted in flow separation and significant turbulence observed in flames. Previous work by Ha et al. found that attaching an extension plate to the leading section of a fuel sample prevented this flow separation and ensured a laminar flow profile incoming to the sample. A 10 cm wide, 40.6 cm long thin, metal lip was therefore mounted from the leading edge of the sample to the outlet of the wind tunnel, providing a laminar diffusion flame that eventually was found to match existing theory⁷.

In testing liquid fuels a porous noncombustible wick was needed. A 10 cm x 10 cm x 1.27 cm thick sheet of Alkaline earth silicate wool was selected for forced flow experiments due to its high porosity and low thermal conductivity. In order to prevent leakage of fuel from the sample, sodium silicate glue was used to apply aluminum foil to all except the front face. The sample was also "baked' to remove organic binders by passing a blowtorch over the sample for approximately 20 minutes, at which point the flame changed from yellow to blue (indicating the removal of binders from the sample). During testing, wicks were soaked with approximately 120 ml of liquid fuel (ethanol or methanol) which was found to be the point of saturation for the 10 cm wide wicks.

The mass burning rate of the fuel was determined by measuring the mass lost from the sample over time during combustion at a rate of 1 Hz. The sample setup was supported over a precision mass balance with a maximum capacity of 32.2 kg and resolution of 0.1 g, fine enough to measure this mass-loss rate with high precision. Following ignition of the sample by a blowtorch, the mass-loss rate of the condensed fuel increases as a function of time, eventually reaching a constant rate which eventually fades toward the end of the test as the fuel burns out. This "steady" region, where evaporation of the fuel rather than diffusion through the wick dominates burning, is the region of interest where data is sampled. For a liquid wick, samples were found to burn with a steady mass-loss rate for approximately 400 sec, approximately the middle 80% of a test. All burning rates presented are averages of at least six repeated tests under specified conditions, where the repeatability of measurements were found to be within 1.2% of the mean.

For testing of a solid fuel sample, polymethyl methacrylate (PMMA) was selected as it burns relatively steadily and does not char. In order to ignite the sample, a blowtorch was passed over the sample surface for 50-60 sec, at which point the entire surface was uniformly ignited. Because the fuel sample was small and the experimental results found to be very repeatable, the method was deemed to be sufficient for ignition. Unlike liquid fuels soaked into a noncombustible wick, solid fuels regress as a function of time and are therefore never truly achieve a steady regime. Instead, early times of burning were chosen to be sampled where the fuel remained relatively flat, experimentally determined to occur during the first 150 sec following ignition.

For both liquid and solid fuels, temperatures over the fuel surface were mapped in the gas phase using fine-wire thermocouples. For PMMA, temperatures were sampled at 6 points above the surface starting from the molten layer into the gas phase at 0.25 mm intervals (for forced convection tests). For liquid fuels, these measurements were performed from the thin layer of fuel at the surface out to 6 points at the same resolution. These profiles were taken at 12 locations along the length of the fuel surface, within 400 sec of ignition for liquid samples and within 150 sec for PMMA.

The aforementioned temperature measurements were carried out using R-type Pt/Pt-13% Rh micro thermocouples (spot welded) with two wire diameters, 50 μm (0.002 in) and 75 μm (0.003 in) having bead diameters of approximately 100 μm and 150 μm, respectively. The size of the thermocouples was chosen such that the thermocouple was as small as possible without recurring breakage (to minimize needed radiation corrections), however some radiation corrections were still necessary. Using two thermocouples of different diameters were chosen in order to better determine an appropriate radiation correction (described later). Micro thermocouples were then traversed using a set of computer-controlled X-Y unislides with a maximum spatial resolution of 1.5 μm. Voltage signals were then were acquired, conditioned and digitized via a data acquisition module rated up to 0.02 °C measurement sensitivity. LabVIEW software was used to synchronize motion of both the 50 μm and 75 μm wire-diameter thermocouples with temperature measurement over the sample.

In order to determine a relatively accurate radiation correction, the two thermocouple sizes described were traversed over the same location during repeated tests. The correlation of Collis and Williams was applied for heat losses from the sample^5-6,8,

     (1)

where Nu is the Nusselt number and Re = Ud_w / v is the Reynolds number, which was obtained for 0.02 < Re < 44, with properties evaluated at the film temperature, Τ_m , an average of the gas, Τ_g, and thermocouple, Τ_tc temperatures. Here, the Reynolds number Re is defined as indicated for the local gas flow velocity U and kinematic viscosity v. d_w in Eq. (1) represents the thermocouple wire diameter.

For steady-state measurements, as in the case described here, an energy balance on the thermocouple junction reduces to a convective-radiative heat balance (neglecting errors due to conduction and catalytic effects), given by

     (2)

     (3)

where Τ_g is the real gas temperature, Τ_tc is the thermocouple junction (or bead) temperature, Τ_surr is the temperature of the surroundings, ε_tc is the emissivity of the thermocouple junction, σ is the Stefan-Boltzmann constant and h is the convective heat transfer coefficient of the flow over the thermocouple junction defined as h = k Nu/d. k is the thermal conductivity of the gas, Nu is the Nusselt number, and d is the thermocouple wire diameter. The choice of the Nusselt number correlation is of paramount importance in calculating a radiation correction to the measured thermocouple temperature because, as shown in Eq. (3), the radiation correction is inversely proportional to the Nusselt number. This choice is complicated, however, due to the existence of multiple "appropriate" Nusselt number correlations and the difficulty in estimation of the properties of the gas mixture surrounding the thermocouple, particularly its thermal conductivity. The bulk of evidence in literature, however, clearly indicates that a cylindrical Nusselt number correlation is most appropriate for describing the convective heat transfer to nearly all practical thermocouples^5-6, preferably that of Collis and Williams⁸.

The Nusselt number correlation must be substituted into a steady state convective-radiative balance (equation 3) and neglecting small temperature dependence, a system of two equations with two unknowns (namely Τ_g and U) are formed,

     (4)

and

     (5)

Equations (4) and (5) must be solved iteratively together at each point, since gas-phase conductivities and kinematic viscosities are both a function of temperature. The bead temperature should be used as the first iteration of gas temperature to evaluate the thermal conductivity and kinematic viscosity, with the iterative value re-taken until low errors are approached. When solving the equations, it appears that the radiation correction (i.e., the difference between the thermocouple reading and the actual temperature) increases for larger diameter thermocouples and is reduced with increasing flow velocities over the bead. d_w1 and d_w2 in Eqs. (4) and (5) represent the thermocouple wire diameters used in our study.

The emissivity of the bead (ε_tc) can also be found as a function of temperature using a method outlined by Jakob⁹. In his analysis, Jakob solves Maxwell's wave equations for the complex indices of refraction on a metallic surface as a function of its electrical resistivity. An assumption is taken in the limit of low resistivity and large indices of refraction, which holds true for metals, yielding a simple correlation for the hemispherical total emissivity of platinum (Pt) as,

     (6)

where, for platinum, r_e ≈ r_e,273T / 273, with T in K and r_e,273 = 11×10^-6 Ω–cm.
Therefore, the platinum emissivity becomes^5-6

     (7)

for 0 < T < 2,330 K. The emissivity of the thermocouple bead or junction, as appears in Eqs. (4) and (5) can therefore be evaluated by using the above expression. An iteration is not necessary for Eqs. (6) and (7) because the actual value of the bead temperature is known, only the gas temperature and velocity in Eqs. (4) and (5) need to be solved iteratively.

During experiments, two thermocouples were traversed exactly to the same measurement points and data was sampled to account for the radiation correction in the temperature measurements. The corrections applied as a result of iterating Eqs. (4) and (5) were small, for example only +79 K for the 50 μm wire-diameter thermocouple at 1,700 K and less than 5 K near the fuel surface⁶. Since the thermocouples also cross regions of high temperature gradients consideration of conduction losses through the wire must also be considered, however due to the small cross sectional areas of the thermocouple wires, such errors were calculated to be < 1%, therefore no corrections were necessary^5-6.

With the fuel surface positioned in the center of the air stream at the exit of the wind tunnel, easy access to the fuel surface was provided for micro thermocouple and hot-wire anemometer measurements. During cold-flow runs of the wind tunnel (no combustion) the free-stream velocity, U_∞ of the wind tunnel was calibrated using a hot-wire anemometer which sampled at a rate of 50,000 samples/sec for a total duration of 10 sec per point. The velocity profile along the outlet of the entire tunnel was taken, revealing that a consistent plug flow emanating from the center of the tunnel outlet. This is expected for a square channel such as the outlet of our wind tunnel. Previous measurements by Sforza et al.¹⁰ showed that the potential core length of a square jet with Reynolds number Re_d between 2.6 and 8.8 x 10⁴ should be about 5 d downstream of the exit, where d is the height of the channel. For d = 30.48 cm, the width of the wind tunnel outlet, Re_d  is between 1.5 x 10⁴ and 3.9 x 10⁴ meaning the sample remains within 1d (20 cm) of the tunnel outlet. The repeatability of these measurements was within 3% of the mean.

Temperatures were measured over the surface of an ignited sheet of 10 cm x 10 cm x 1.27 cm PMMA placed at the outlet of a wind tunnel operating at U_∞ = 0.79 m/sec and 2.06 m/sec. The procedures outlined above were used to capture temperature measurements which were non-dimensionalized in terms of normal length y^*=y/L and temperature, T* = (T – T_w,p / T_fl,ad – T_w,p), where Τ_w,p and Τ_fl,ad  represent the wall and adiabatic flame temperatures, respectively for a given fuel, y the position normal to the fuel surface where the temperature is measured and L the length of the fuel surface. The non-dimensional temperature gradients normal to the surface were then calculated, (∂T* / ∂y*)_y*=0 by fitting a fifth-order polynomial to the non-dimensional temperatures and extracting the slope at the fuel surface, y^*=0.

Figure 2 (a) shows these non-dimensional temperature gradients along the length of the fuel surface. They are clearly highest at the leading edge of the fuel surface, where the flame is closest to the fuel surface, and decrease toward the trailing edge (x = 100 mm), where the flame is farthest from the fuel surface. The non-dimensional temperature gradients can be used to determine the local mass-burning rate by applying the correlation^4,6,

     (8)

where B is the mass transfer number of the given fuel, k_w the thermal conductivity of air evaluated at the wall temperature, c_p the specific heat of the air evaluated at an adiabatic flame temperature of the fuel, and L the length of the pyrolyzing fuel surface. The local mass burning rate is then found to vary in a manner similar to the non-dimensional temperature gradients, shown in Figure 2 (b).

Unlike liquid fuels, for PMMA the local mass-burning rate can also be approximated a posteriori by measuring local surface regression over fixed intervals of time^2,11. PMMA samples were burned under representative conditions for periods of time starting at 50 sec and increasing at 50 sec intervals followed by extinction of the sample. The pyrolysis mass flow rate for PMMA is computed at each x location along the central symmetry axis using a first-order approximation given by Pizzo et al.¹¹, discussed in the literature elsewhere^4-6. An average density of PMMA, ρ_s = 1,190 kg/m³ was used along with measured surface regression along the fuel surface to arrive at mass-loss rates during each 50 sec interval along the length of the fuel sample. Although a shorter time step would be desirable, errors in measurement make it become impractical when time steps are less than 50 sec⁵.

To compare local mass-loss rates from thermocouples with those from regression profiles, data from fuel burnout times of 100 and 150 sec were used to compare the local mass burning rates shown in Figure 2 (b). These times correspond to approximately the same times these measurements were taken. As can be seen in the figure, both methods of measuring the local mass burning rate appear very close to one another, suggesting the methodology works well for these types of flames.

For convectively-dominated flames such as these small, laminar ones, temperature gradients at the fuel surface can also be used to extract convective heat fluxes as they are, in essence, directly related to the temperature gradient at the surface. Using measured mass-loss rates, components of flame heat flux can also be extracted along the pyrolysis zone. Using several approximations to the heat balance at the fuel surface, listed in literature elsewhere^2-3, these components can be determined over the surface of a burning slab of PMMA. Figure 3 shows this result, for a PMMA flame stabilized with an ambient free-stream velocity of U_∞= 2.06 m/sec. The technique can therefore be extremely useful in evaluating several measures to describe the burning of small samples of fuels, leading to increased understanding of the combustion process, particularly the relationship between the solid and gas phase.

Figure 1. Experimental Setup. (a) Schematic of the experimental setup used to measure mass-loss rates and temperature profiles over a forced-convection boundary layer diffusion flame. (b) Experimental setup for investigating boundary layer diffusion flames under forced flow. Please click here to view a larger version of this figure.

Figure 2. Temperature Gradient and Local Burning Rate Results. (a) Variation of the normal non-dimensional temperature gradients along the fuel surface for a PMMA boundary layer diffusion flame at U_∞= 0.79 m/sec and 2.06 m/sec, respectively. (b) Variation of the local mass-burning rates for PMMA boundary layer diffusion flames at different free-stream conditions. Local mass burning rates obtained through non-dimensional temperature gradients is compared against the experimental data obtained through regression of the PMMA surface. Please click here to view a larger version of this figure.

Figure 3. Heat Flux Results under Forced Flow. Distribution of various components of flame heat flux in the pyrolysis zone for a PMMA boundary layer diffusion flame at U_∞= 2.06 m/sec. Please click here to view a larger version of this figure.