Steady Laminar Flamelet Model Research Articles

Numerical investigation to evaluate the effects of gravity and pressure on flame structure and soot formation of turbulent non-premixed methane-air flame

In this study, a turbulent non-premixed (diffusion) methane-air flame has been investigated computationally to analyze the influences of pressure and gravity on flame structure and sooting characteristics between 1 and 10 atm. The simulation has been conducted in a 2-D axisymmetric computational domain using the finite volume-based computational fluid dynamics (CFD) code. The interaction of turbulence and chemistry is modeled by considering the steady laminar flamelet model (SLFM) and the GRI Mech 3.0 chemical mechanism. The radiative heat transfer calculation is carried out by considering the discrete ordinate (DO) method and the weighted sum grey gas model (WSGGM). The semi-empirical Moss-Brookes model is considered to calculate soot. The impact of gravity on flame and sooting characteristics are evaluated by comparing the normal-gravity flames with the zero-gravity flames. The effect of soot and radiation on flame temperature is also examined. The results show a close agreement with the measurement when both soot and radiation are included in the numerical modeling. The rates of soot formation, surface growth, and oxidation increase with increased operating pressure, regardless of gravity. Zero-gravity flames have a higher soot volume fraction, a wider soot-containing zone, a higher CO mass fraction, and a lower flame temperature than normal-gravity flames while maintaining constant pressure. In normal-gravity flames, the CO mass fraction decreases with pressure, whereas it increases with pressure rise in flames of zero gravity. Flames of zero gravity appear taller and broader compared to the flames of normal-gravity for a fixed pressure. An increase in pressure significantly reduces the flame length and width in normal-gravity flames. However, the pressure elevation has little effect on the shape of a zero-gravity flame. The outcomes of the present study will assist in fully understanding the combustion and sooting characteristics of turbulent diffusion flames that will help design and develop high-efficiency, pollutant-free combustion devices and fire suppression systems for space application.

A new acid gas destruction kinetic model for reaction furnace of an industrial sulfur recovery unit: A CFD study

• Developing a reduced reaction mechanism for acid gas combustion. • Simulating detailed full-scale reaction furnace with new reduced kinetic model. • Predicting accurate results in terms of temperature profile and chemical species. • Vectorwall and co-directional diffuser showed the lowest radiative heat flux. • Common checkerwall and co-directional diffuser showed the highest H2S efficiency. A new reduced kinetic model is developed for the simulation of acid gas destruction in the industrial reaction furnace of sulfur recovery units. The proposed CFD model includes the reactions of the new kinetic mechanism, steady laminar flamelet model, and fine details of industrial furnace geometry related to the burner, choke ring, checkerwall, and exhaust pipe holder. The mean relative error in predicting H 2 S conversion using CFD, coupled with our new kinetic model, is about 9.48% when compared with the industrial data. The influences of two types of burners and the checkerwalls on the thermohydrodynamics behaviors of the reaction furnace are investigated. The reactor equipped with Vectorwall and co-directional diffuser shows the lowest radiative heat flux (RHF) and favorable outlet temperature to protect the tube sheets, while the one with conventional checkerwall and co-directional diffuser shows the highest H 2 S conversion efficiency in the furnace.

Modelling extinction/re-ignition processes in fire plumes under oxygen-diluted conditions using flamelet tabulation approaches

The main objective of this article is to investigate the capability of the flamelet progress variable (FPV) model to capture the extinction processes observed in under-ventilated fire scenarios. To this end, large eddy simulation (LES) of the methane line fire plumes in oxygen-reduced environments down to global extinction, investigated experimentally at the University of Maryland (UMD), is performed. Two experimental burner configurations, that differ by the presence (anchored) or not (non-anchored) of an oxygen anchor to stabilise the flame base, are considered leading to two different extinction modes. Both the FPV and the steady laminar flamelet (SLF) model coupled with a presumed filtered density function (FDF) are considered. The Rank Correlated Full Spectrum k-distribution (RCFSK) model is used as a gas radiative property model. In both non-anchored and anchored scenarios, the FPV model reproduces with fidelity the evolution of the fire plume structure, radiative loss, and combustion efficiency with decreasing down to global extinction, without introducing any adjustable constant. The extinction in the non-anchored scenario occurs owing to flame-based detachment coupled to the generation of a buoyancy-driven vortex and is found to be very sensitive to the grid resolution in the near burner region. The present results suggest that these processes can be adequately resolved with a spatial resolution of 2.5 mm in this region. The SLF model, for its part, provides reliable predictions comparable to the FPV as long as no local extinction/re-ignition process occurs.

Investigation on combustion characteristics and emissions of biogas/hydrogen blends in gas turbine combustors

In the present work, numerical investigations are performed to study the combustion characteristics of biogas fuel blended with hydrogen at various compositions for a non-premixed swirling flame in a can-type gas turbine combustor. The amount of hydrogen enrichment varies from 0 to 50% by volume. A numerical approach using the non-premixed flamelet model, turbulent standard (k–ε) model, and P-1 radiation model was adopted for simulating the can-type combustor power at a fixed operating power of 60 kW. The steady laminar flamelet model was used to analyze the effect of hydrogen enrichment, global equivalence ratio with different swirl numbers on a stable flame operation, temperature distribution and contours, velocity streamline contours, NO emissions, and species concentrations. The results indicate that hydrogen enrichment and the variation of the equivalence ratio and the swirl numbers significantly impacted the flame macrostructure. Hydrogen enrichment in the fuel intensifi combustion, leading to higher flame temperature and wider flammability than bure biogas. Maximum NO emissions in the outlet chamber have been dropped by 43 and 78 (ppm @15 % by volume of O2) for the biogas and biogas-50% H2, respectively, due to the reduced flame temperature leading to reduction in thermal NOx formation with reduction equivalence ratio from 0.5 to 0.2. The flame temperature and NO emissions at ϕ=0.2 with a high rate of hydrogen (50% H2) are close to the results of pure biogas (0% H2) at the same equivalence ratio. The results show that CO and CO2 emissions decrease with increasing hydrogen addition and decreasing the equivalence ratio; due to a decrease in the amount of carbon, the cooling effect, and an increase in the OH concentration.

Conditional moment closure method with tabulated chemistry in adiabatic turbulent nonpremixed jet flames

The conditional moment closure (CMC) method with tabulated chemistry is proposed to reduce the computational load for integration of stiff reaction steps in the conventional CMC methods. It is based on the assumption that temperature and all species except CO and CO2 adjust fast enough so that they can be uniquely determined by the single reaction progress variable given as the sum of CO and CO2 mass fractions. The CMC equations are solved for the conditional reaction progress variable, Qpv, whereas the other species mass fractions and the reaction rates including that for Qpv are retrieved from lookup tables. A steady homogeneous form of the conditional variance and covariance equations are solved to construct the second-order closure table to be consistent with Steady Laminar Flamelet Model (SLFM)-based first-order closure. Good agreement is shown between the results by integrated and tabulated chemistry in both the first-order and the second-order CMC for Sandia Flames D, E and F. The overall computational time is reduced to about 0.5% of that by the conventional CMC method involving integration of the detailed reaction mechanism for all species and temperature.

Effect of the Preheated Oxidizer Temperature on Soot Formation and Flame Structure in Turbulent Methane-Air Diffusion Flames at 1 and 3 atm: A CFD Investigation

This article presents the results of computations on pilot-based turbulent methane/air co-flow diffusion flames under the influence of the preheated oxidizer temperature ranging from 293 to 723 K at two operating pressures of 1 and 3 atm. The focus is on investigating the soot formation and flame structure under the influence of both the preheated air and combustor pressure. The computations were conducted in a 2D axisymmetric computational domain by solving the Favre averaged governing equation using the finite volume-based CFD code Ansys Fluent 19.2. A steady laminar flamelet model in combination with GRI Mech 3.0 was considered for combustion modeling. A semi-empirical acetylene-based soot model proposed by Brookes and Moss was adopted to predict soot. A careful validation was initially carried out with the measurements by Brookes and Moss at 1 and 3 atm with the temperature of both fuel and air at 290 K before carrying out further simulation using preheated air. The results by the present computation demonstrated that the flame peak temperature increased with air temperature for both 1 and 3 atm, while it reduced with pressure elevation. The OH mole fraction, signifying reaction rate, increased with a rise in the oxidizer temperature at the two operating pressures of 1 and 3 atm. However, a reduced value of OH mole fraction was observed at 3 atm when compared with 1 atm. The soot volume fraction increased with air temperature as well as pressure. The reaction rate by soot surface growth, soot mass-nucleation, and soot-oxidation rate increased with an increase in both air temperature and pressure. Finally, the fuel consumption rate showed a decreasing trend with air temperature and an increasing trend with pressure elevation.

Mixing and combustion at low heat release in large eddy simulations of a reacting shear layer

In this paper, the mixing and combustion at low-heat release in a turbulent mixing layer are studied numerically using large eddy simulation. The primary aim of this paper is to successfully replicate the flow physics observed in experiments of low-heat release reacting mixing layers, where a duty cycle of hot structures and cool braid regions was observed. The nature of the imposed inflow condition shows a dramatic influence on the mechanisms governing entrainment, and mixing, in the shear layer. An inflow condition perturbed by Gaussian white noise produces a shear layer which entrains fluid through a nibbling mechanism, which has a marching scalar probability density function where the most probable scalar value varies across the layer, and where the mean-temperature rise is substantially over-predicted. A more sophisticated inflow condition produced by a recycling and rescaling method results in a shear layer which entrains fluid through an engulfment mechanism, which has a non-marching scalar probability density function where a preferred scalar concentration is present across the thickness of the layer, and where the mean-temperature rise is predicted to a good degree of accuracy. The latter simulation type replicates all of the flow physics observed in the experiment. Extensive testing of subgrid-scale models, and simple combustion models, shows that the WALE model coupled with the Steady Laminar Flamelet model produces reliable predictions of mixing layer diffusion flames undergoing with fast chemistry.

Characterization of a Novel Elliptical Air-port Inverse Jet Flame

ABSTRACT This paper reports the experimental and numerical investigation of an inverse jet flame (IJF) burner with an elliptical central port and circumferentially arranged circular fuel ports (CAFP). In order to enhance the air-fuel entrainment, a passive technique using an elliptical central jet is implemented. The flame appearance of elliptical central air-port IJF denoted a difference in the jet spread on major and minor axis planes. The azimuthal structure of elliptical central port IJF exhibited properties similar to elliptical normal jet flames. The experiments also revealed that, unlike in circular central port IJF burner, elliptical IJF generates a wide range of turbulent scales beneficial for combustion applications as visualized through schlieren images. The numerical model based on a steady laminar flamelet model and the standard k-ε model having a modified model constant predicted the thermal characteristics of elliptical central port CAFP IJF. The experiments reported a significant reduction in flame height for IJF with an elliptical central port due to differences in spreading and entrainment rates. Thermal and emission characteristics are significantly different compared with circular IJF for a similar momentum flux ratio. Interestingly, the elliptical central port IJF demonstrates a lower NO emission index at higher and lower momentum flux ratios. Apart from the temperature, flame height, and NO emission index variation, the mixing and entrainment characteristics on major and minor axis planes are vividly illustrated and quantified as compared to the conventional design has been brought out explicitly.

Effect of burner angle on the heat transfer of a frit furnace

In this work, a numerical analysis was performed about the effect of a flat-flame burner incidence degree on the heat transfer of an industrial scale frit melting furnace, which uses a flat-flame natural gas oxy-combustion burner. The thermal performance of the furnace was evaluated by predicting the temperature distributions, the recirculation of the combustion gases, and the heat flow to the load, using three different geometrical configurations, differing in the inclination of the burner at 0°, 3.5°, 7° with respect to the longitudinal axis. The simulations were carried out using the ANSYS® Fluent software. The Steady Laminar Flamelet (SFM) model, the k-epsilon realizable model, and the discrete ordinates model were used to model combustion, turbulence, and radiation, respectively. The weighted model of the sum of gray gases (WSGGM) was used for the coefficient of absorption of the combustion species. It was observed that the furnace temperature estimated with the simulations is similar to that found in the actual process. Additionally, the simulations showed that for the angle of 7°, the flame collides with the frit, which could generate deposition of frit particles in the internal walls of the furnace; this would affect the emissivity of the refractory material. The 3.5degree angle showed a better distribution of heat flow to the frit and recirculation rate compared to the burner at 0° and 7°.

Real-Gas-Flamelet-Model-Based Numerical Simulation and Combustion Instability Analysis of a GH2/LOX Rocket Combustor with Multiple Injectors

A large eddy simulation (LES) and combustion instability analysis are performed using OpenFOAM for the multiple shear-coaxial injector combustor DLR-BKD (in German Deutsches Zentrum für Luft–Brennkammer D, German Aerospace Center–Combustion Chamber D), which is a laboratory-scale combustor operating in a real-gas environment. The Redlich–Kwong–Peng–Robinson equation of state and steady-laminar flamelet model are adopted in the simulation to accurately capture the real-gas combustion effects. Moreover, the stable combustion under the LP4 condition is numerically analyzed, and the characteristics of the combustion flow field are investigated. In the numerical simulation of the combustion instability, the instability is generated by artificially superimposing the 1st transverse standing wave solution on the stable combustion solution. To decompose the combustion instability mode, the dynamic mode decomposition method is applied. Several combustion instability modes are qualitatively and quantitatively identified through contour plots and graphs, and the sustenance process of the limit cycle is investigated.

Numerical Simulation of a GH2/LOx Single Injector Combustor and the Effect of the Turbulent Schmidt Number

A large-eddy simulation (LES) of a gaseous hydrogen/liquid oxygen (GH2/LOX) single-injector rocket combustor is performed in this study. The Redlich–Kwong–Peng–Robinson (RK–PR) equation of state is used to simulate the real-gas effect under high-pressure conditions, and the steady laminar flamelet model (SLFM) is implemented to simulate fast chemistry, such as a H2/O2 reaction. From the numerical simulation, the characteristics of time-averaged flow and flame fields are obtained, and their relationship with the real-gas effect is investigated. It is possible to investigate unsteady flame features and the mixing mechanism of propellants in detail by examining multiple snapshots of the field contour. Another purpose of the study is to investigate the differences in flow and flame structures according to the variation in the turbulent Schmidt number. By comparing the simulation result with the natural OH* emission image and temperature profiles from experimental data, the appropriate range of the turbulent Schmidt number for the simulation is obtained. Furthermore, this paper suggests the usefulness and validity of the current research by quantitatively comparing (i.e., temperature profiles) numerical results with those of existing literature.

Comparison between numerical and experimental data of the radiative heat transfer in a natural gas/CO2/H2 turbulent flame

Accurate computation of the radiative heat flux emitted by turbulent flames involves the challenging modeling of turbulence-radiation interactions (TRI). This study considers a non-premixed turbulent flame, in which the fuel is natural gas with CO2/H2 dilution and ambient air as the oxidant. The radiative exchange is numerically solved using the weighted-sum-of-gray-gases (WSGG) gas model, and the discrete ordinates method for directional integration of the radiative transfer equation (RTE). The steady laminar diffusion flamelet (SLDF) model is used to solve the chemical kinetics. To account for the turbulence-chemistry interaction, the mean scalars are calculated by a presumed probability density function (PDF) approach. Turbulence is treated with the k-ε standard model. The impact of TRI modeling is performed employing two methodologies. The first one is based on the correlation between the absorption coefficient and the temperature self-correlation, considering that the absorption coefficient is only dependent on the mean local temperature. The second one considers the dependence of the absorption coefficient with both the mean temperature and the species mole concentrations. The temperature variance is obtained in two ways, using a transport equation and directly from the PDF approach. Five sets of numerical results are compared with measured experimental data for the radiative heat flux. The solution is obtained using ANSYS/Fluent code coupled with user-defined functions (UDFs) to compute RTE/WSGG/TRI formulations.

Evaluation of air curtain and emergency exhaust system for smoke confinement of an enclosure

This paper analyses the various configuration for the emergency ventilation system consisting of an air curtain and exhaust fan to manage the dispersion of heat and toxicity inside an enclosure for different fire scenarios. Employing this ventilation system is helpful to secure an escape route or extinguishing the fire. The air curtain discharge velocity is 10, 18, and 30 m/s and its discharge angle is set to be 0°,15°, and 30°. Three values of 0.5, 1, and 2m3/s are considered for the exhaust flow rate. Computational Fluid Dynamics simulations have been conducted with a steady laminar flamelet model and buoyant standard k−ε turbulence model to assess the performance of the air curtain and emergency exhaust system for smoke confinement. Evaluation of an optimized state of the emergency ventilation system is provided by the Taguchi method due to computational limitations in solving various cases for the ventilation system configuration. Results show that for each location and heat release rate of fire, it is possible to manage heat, CO, and CO2 dispersion with the adjustment air curtain parameters and emergency exhaust system. Finally, the optimum state of the system is reported for each scenario, and the temperature and concentration of toxic gas have been compared. Results show that for the 200 kW fire, 2 m3/s exhaust flow rate with air curtain discharge velocity of 18 m/s and 15° would be adequate. However, 500 kW fire requires 30 m/s with 30° discharge velocity to contain the fire inside the compartment.

Effect of dividing single flare tip into multiple tips on soot reduction

Several methods are applied for soot reduction in industrial flares. However, they usually involve other issues such as flame safety and other pollutant formations; therefore, they should be handled carefully. Splitting flare tip into multiple branches is an idea that is thought to reduce soot formation by increasing the contact surface and providing better mixing. In this study, changing a single tip of an industrial flare into multiple tips was investigated by Computational Fluid Dynamic software Ansys Fluent 18. Reynolds Average Navier–Stokes approach was used to model the fluid flow, and its turbulence was modeled by realizable k–e model. The steady laminar flamelet model was chosen as the combustion model. Soot formation was modeled using Moss–Brookes approach, and validated by comparing the simulation results with available experimental data. Effects of tip diameter, number of branches, and distance between branches on soot and NOx yields, and flame stability were studied. According to the results, increasing the number of branches having larger diameters by taking flame stability limitations into consideration, and choosing optimum distances between branches caused significant soot reduction without noticeable changes in the NOx formation.

Entrainment studies in inverse jet flame port burner

The present investigation aims to investigate the fundamental understanding of entrainment characteristics of a Circumferentially Arranged Fuel Port Inverse Jet Flame Burner (CAFP IJF). The high-speed flame Schlieren visualization is carried out experimentally for 8, 18 and 32 port CAFP IJF burner for varying air–fuel operating conditions to visualize the entrainment characteristics. The region of fuel entrainment is found to occur within the base region whereas intense mixing and combustion is observed in transition and main flame region respectively. The 32 port CAFP IJF burner exhibits enhanced entrainment characteristics and augmented ambient air–jet interactions for similar operating conditions as compared to a lesser number of circumferential fuel ports. The jet breakup length is employed to identify the interaction of ambient air with the combustion driven vorticial structures. The steady laminar flamelet model is used to investigate the entrainment characteristics of a 32 port CAFP IJF burner. The calculated entrainment coefficients at different operating conditions for reacting and non-reacting CAFP IJF indicate that the entrainment rate for reacting jet is lower due to the diminution of density across the flame cross-section at each axial plane. The strong ambient air entrainment is observed within the interstitial space between consecutive fuel ports which promote air–fuel mixing. Additionally, unlike in Normal Jet Flame (NJF), a clear distinction between air and fuel entrainment is found to be essential for the current CAFP IJF burner configuration.

Comparison of combustion models based on fast chemistry assumption in large eddy simulation of pool fire

In the present study, OpenFOAM software was adopted to implement a solver using the Steady Laminar Flamelet Model (SLFM) and Eddy Dissipation Concept (EDC) combustion models. Afterward, the compatibility of fast chemistry-based combustion models consisting of the Infinitely Fast Chemistry, Eddy Dissipation Model (EDM), EDC, and SLFM combustion models was studied in the simulation of 2.7 MW methane pool fire, by employing a one-equation sub-grid-scale turbulence model. Comparing the results against experimental data indicates that the SLFM model anticipates more flame width, and it is capable of predicting the mean turbulent kinetic energy with the maximum error of 4–8%. On the other hand, the EDM model can attain the mean vertical velocity of the flow in the range of 5–10% which is more accurate than the other models. Furthermore, the puffing frequency was derived by the Fast Fourier Transform analysis of vertical velocity, pressure, and temperature in a given time for each of these models. EDM and EDC combustion models illustrated a relative error of 7%, in predicting puffing frequency, compared to experimental results.

REDIM reduced chemistry for the simulation of counterflow diffusion flames with oscillating strain rates

The dynamic behaviour and structures of laminar counterflow diffusion methane flames under oscillatory strain rates are investigated based on both detailed and reduced chemistry. It is known both from experiment and numerical studies that flame can deviate from its quasi-steady manner for high frequencies, which makes the well-known steady laminar flamelet model questionable. In this work, the Reaction-diffusion manifolds (REDIM) concept for simplified chemistry is applied to study the laminar counterflow diffusion flames with oscillating strain rates. In the construction of REDIM, one needs little knowledge of the studied system, and the REDIM reduced chemistry can cover both stable and unstable (extinction) regimes of the studied system. It is shown that the REDIM can capture both the steady and unsteady behaviours of the flame structures even for high frequencies, where the standard laminar steady flamelet approach is not appropriate.

Assessment of various tar and soot treatment methods and a priori analysis of the steady laminar flamelet model for use in coal combustion simulation

Soot formed in the fuel-rich regions of coal flames is known to have a significant impact on the radiative heat transfer characteristics of the flame. It is therefore important to account for the effect of soot radiation when simulating coal combustion systems. Several recent coal combustion studies have used acetylene as a surrogate for devolatilized tar and neglect soot formation altogether, while others have utilized empirical models for tar and soot or even chemical mechanisms which include tar and soot as species. In this work, we investigate several methods of treating coal-derived tar and soot and the impact each treatment has on predicted furnace temperature, particle mass loss, and other quantities of interest. Furthermore, we perform a priori comparisons of simulation results to calculations from a steady laminar flamelet model in order to assess the accuracy of a flamelet approach for each tar and soot treatment considered. Data used as a basis for the study is generated through One-Dimensional Turbulence (ODT) simulation of a coal combustion system in which high-fidelity models are used for gas phase chemistry and devolatilization, where char combustion is neglected.

Effects of hydrogen enrichment of methane on diffusion flame structure and emissions in a back-pressure combustion chamber

In the present study, the effects of hydrogen enrichment of methane are investigated numerically from the diffusion flame structure and emissions aspect. Fluent code is utilised as the simulation tool. In the first part of the study, four experiments were conducted using natural gas as fuel. A non-premixed burner and a back-pressure boiler were utilised as the experimental setup. The natural gas fuel consumption rate was changed between 22 Nm3/h and 51 Nm3/h. After the experimental studies, the numerical simulations were performed. The non-premixed combustion model with the steady laminar flamelet model (SFM) approach was used for the calculations. The methane-air extinction mechanism was utilised for the calculation of the chemical species. The numerical results were verified with the experimental results in terms of the flue gas emissions and flue gas temperature values. In the second part of the study, four different hydrogen-enriched methane combustion cases were simulated using the same methane-air extinction mechanism, which included the hydrogen oxidation mechanism as a sub mechanism. The same energy input (432 kW) was supplied into the boiler for all the studied cases. The obtained results show that the hydrogen addition to methane significantly change the diffusion flame structure in the combustion chamber. The hydrogen-enriched flames become broader and shorter with respect to the pure methane flame. This provides better mixing of the reactants and combustion products in the flame regions due to the use of a back-pressure boiler. In this way, the maximum flame temperature values and thermal NO emissions are reduced in the combustion chamber, when the hydrogen addition ratio is less than 15% by mass. The maximum temperature value is calculated as 2030 K for the case with 15% hydrogen addition ratio by mass, while it is 2050 K for the case without hydrogen enrichment. Therefore, it is determined that the hydrogen-enriched methane combustion in a back-pressure combustion chamber has the potential of reducing both the carbon and thermal NO emissions.

Numerical studies of turbulent swirling reacting flows using LES and URANS

Numerical studies of turbulent swirling reacting flows are performed using unsteady Reynolds-averaged Navier-Stokes (URANS) and large-eddy simulation (LES) approaches. Aiming at the reduction of computational costs, the present research assesses the feasibility of URANS for the computations of turbulent reacting flows. The conserved scalar-mixture fraction-based thermo-chemical variables are described using the steady laminar flamelet model. The Favre-filtered scalars are obtained from the presumed beta probability density function (β–PDF) approach. The flow field exhibits upstream recirculation zone due to the bluff body and a downstream vortex breakdown region induced by the swirling flow. The study reveals that the strength of the vortex decays with the increase of distance from the injection region. The temperature exhibits high values in the region surrounding the flame. The present research shows that in spite of its low computational cost, the URANS approach is quite dissipative when compared with LES. Therefore, LES is a more appropriate approach for the numerical simulation of turbulent combustion, when the solution accuracy is of concern.