Analysis Of Airflow Resistance On Longwall Faces

Introduction In the design and specification of a ventilation system for an underground mine, it is necessary to make reasonably accurate estimates of the pressure losses in the various airways of the mine. These estimates can be made with little difficulty for open airways with simple geometric cross-sections, such as those cut by continuous miners or tunnel-boring machines. The situation is much different on a longwall face, where the airway's complex geometric cross section and the presence in the airway of obstructing equipment having a variety of shapes make it difficult, if not impossible, to estimate pressure loss using traditional methods of calculation. Head losses in mine entries are calculated using Atkinson's Equation. [22H= KPLQ (English) H= KP 3Q (SO (1) 5.2AA] where H = pressure loss, in. of H2O (Pa); K = friction factor, lbf•min2/ft4 (kg/m3); P = perimeter, ft (m); L = airway length, ft (m); Q = airflow quantity, ft3/min (m3/sec); and A = flow cross-sectional area, ft2 (m2) In this equation, the friction factor, K, is an empirical constant that describes the aerodynamic roughness of the airway. Typically, the K-factor for a given airway is determined by measuring the factors H, P, L, Q and A in Equation (1) and calculating K. Tables of friction factors calculated in this way are found in textbooks and handbooks that deal with mine ventilation analysis. Unfortunately, very few K-factors have been measured on longwall faces, and the accuracies of those that have been measured are entirely site specific, because of the wide variety of equipment found on longwalls. The development of a technique for prediction without mine-site measurements of the friction factor for any longwall face, regardless of its configuration, will thus be very useful in the design of ventilation systems for mines in which longwall mining is practiced. Calculation of pressure losses using Atkinson's Equation (1) and empirically determined K-factors provides accurate and useful approximations in cases where the airways have relatively simple cross sections. However, a careful analysis using the principles of fluid mechanics shows that such calculations are based on two assumptions that are not strictly correct when there are obstructions in the airway. The first assumption is that the air velocity distribution in the cross section, particularly around the perimeter, is uniform. This assumption results from the fact that the tabulated K-factor values found in the literature are based on field measurements with uniform conditions. Such uniformity does not exist in longwall airflows. The second common assumption is that the K-factor, and corresponding head loss, is independent of the Reynolds Number (NR) for a given flow. In fact, this assumption is not strictly correct, and is particularly erroneous in the case of irregular protuberances into the airflow, such as those found on a longwall face. The errors arising from the assumptions may be avoided by using K-factors calculated by a newly devised method, described below, which takes into account the fundamental principles of aerodynamic drag analysis. This new technique has two advantages: first, it is flexible enough to model any longwall, regardless of equipment configuration; second, it employs terminology and equations familiar to those who perform mine ventilation analysis, using K-factors, for which ventilation engineers have an intuitive understanding, rather than drag coefficients. To provide guidance for development of a longwall drag model, data were taken on two modern longwalls operating in substantially different conditions. Pressure measurements at Mine B were made with 200-foot (61-m) sections of 1/8-in. (3-mm) diameter plastic tubing, attached to a Dwyer Magnehelic gauge. Pressure drops were measured in 200-foot increments down the face, and summed to give the drop for the entire face length. This technique was found to produce small, repeated errors because of the number of segments required to span the longwall. At Mine A this problem was avoided by using a single, continuous, plastic tube for the entire face length. The psychrometric properties of the air were measured for both Mines A and B. A calibrated, standard vane-anemometer was used to measure the airflow on both faces. Finally, numerous dimensions were measured on both faces, and face profile drawings were obtained to allow detailed evaluation of the face equipment geometry. From this information, accurate evaluations of the average wetted perimeter and average area of the longwall face airways were made. Since the airflow is not confined to inside the powered supports at all points along the face, a quadratically weighted average of the airflows measured at various stations along the face was calculated: [n2Qavg =Qi Ii / It(2)i=1] where [Q, avg = average airflow for analytical purposes, ft3/min (m3/sec); Q= airflow at station i, ft3/min (m3/sec); 1= length of segment represented by Q, ft (m); h= length of longwall face, ft (m): and n= number of quantity measurement stations.] The quadratic weighting scheme was chosen because the