Theoretical Description of a New Method of Optimal Program Design

1981 ◽  
Vol 21 (04) ◽  
pp. 425-434 ◽  
Author(s):  
Stefan Miska ◽  
Pal Skalle
Keyword(s):  
Reynolds Number ◽  
Objective Function ◽  
Flow Rate ◽  
Program Design ◽  
Impact Force ◽  
Nozzle Diameter ◽  
General Description ◽  
Rate Of Penetration ◽  
Jet Impact ◽  
Jet Velocity

Abstract Drilling hydraulics have considerable effect on the rate of penetration. Previous studies have examined this problem; however, the effects of differential pressure and reliability of pumping equipment usually were neglected. This paper gives a general description of hydraulic drilling parameters optimized when both these effects were considered. To derive the necessary conditions for optimal hydraulics a nonlinear programming method was applied. Introduction In the rotary drilling process the rock must be fractured at the bottom of the hole. To allow further fracturing and drilling progress, the cuttings must be removed from the bottom efficiently and transported toward the surface. For these purposes, both mechanical and hydraulic energy are brought from the surface to the rock face and should be applied in optimal manner. Previous work in drilling hydraulics has established that this has considerable influence on the rate of penetration as well as on other indicators of drilling efficiency. For that reason, this topic has been a subject of several investigations, both theoretical and experimental. Optimal hydraulics is the proper balance of hydraulic elements that satisfy some criterion of estimation (the objective function). For given drilling fluid properties, these parameters are flow rate (q) and equivalent jet bit nozzle diameter (de). Hydraulic quantities commonly used to characterize jet bit performance include hydraulic horsepower, jet impact force, jet velocity, and Reynolds number at the bit nozzles. However, all these hydraulic quantities are determined when the flow rate and equivalent nozzle diameter have been established. Briefly, the methods of optimal hydraulics program design can be divided in two groups:methods which depend on determining the bottomhole cleaning required, usually bit hydraulic horsepower, to balance the mechanical energy level, andmethods which assume maximization of an arbitrarily established criterion of estimation. Methods in Group 1 have limited application during drilling program design since the required level of hydraulic horsepower, for given mechanical parameters (weight-on-bit and rotary speed combinations) in a particular formation interval, require field tests and thus they cannot be applied before drilling. This method is indicated in Fig. 1. Fullerton has balanced the mechanic and hydraulic energy by means of the "constant drilling energy" concept, valid for some formation types. The various criteria to be maximized in Group 2 are hydraulic horsepower, jet impact force, jet velocity, and Reynolds number. The basic work on this topic was published by Kendall and Goins. Methods for selecting proper nozzle sizes and flow rams are given for each criterion of estimation except the Reynolds number. The latter criterion is discussed by other authors, but they discussed optimal flow rates and equivalent nozzle diameter only for the constant pump pressure range. It was shown that using maximum Reynolds number at the bit nozzles as an objective function for optimal hydraulic program design gives the same result as for maximum jet impact force. SPEJ P. 425^

Investigation of Circular Water Jet Impingement Heat Transfer

2011 ◽  
Author(s):  
Cuicui Liu ◽  
Zeyi Jiang ◽  
Xinxin Zhang ◽  
Qiang Ma ◽  
Yusheng Sun
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Flow Rate ◽  
Water Flow Rate ◽  
Jet Impingement ◽  
Water Jet ◽  
Nozzle Diameter ◽  
Constant Flow Rate ◽  
Impingement Heat Transfer

Mathematical model combining theoretical analysis approach and differential numerical solving techniques has been set up to predict the free surface water jet impingement heat transfer. Heat transfer properties are obtained and validated by comparison with experiments. The characteristic of Nu-r/d distribution is discussed and the effect of nozzle diameter is analyzed. In addition, nozzle arrangements are studied for water jet equipment designation purpose. The results show that: Reynolds number is the dominate parameter in Nu-r/d distribution and area-averaged Nusselt number increases with increasing nozzle diameter. The best heat transfer effect appears when the aspect ratio of rectangular surface equals to 1. Fewer nozzles and bigger single impinged area could get larger Nusselt number under a given total water flow rate and given total impinged area. At a constant flow rate, larger nozzle diameter and smaller Reynolds number present a larger Nusselt number.

Effects of Dilution and Nozzle Diameter on Laminar Dimethyl Ether Lifted Flames

2013 ◽  
Author(s):  
Jie Zhou ◽  
Yuhua Ai ◽  
Wenjun Kong
Keyword(s):  
Mass Flow Rate ◽  
Dimethyl Ether ◽  
Mole Fraction ◽  
Flow Rate ◽  
Nozzle Exit ◽  
Nozzle Diameter ◽  
Nitrogen Dilution ◽  
Lifted Flames ◽  
Inner Diameter ◽  
Jet Velocity

This work aimed at studying the effects of nitrogen dilution and nozzle exit inner diameter on the liftoff properties of the dimethyl ether (DME) jet diffusion flames. The liftoff properties including the liftoff position (HL), the critical liftoff velocity (Ulo) and the critical blowout velocity (Ubo) were studied experimentally. In nitrogen dilution experiments, a slowly converging nozzle was used with inner exit diameter of 0.43 mm. When mole fraction of N2 (Z) increased, a) HL increased because the dilution reduced the chemical activity of fuel, in order to achieve stoichiometric conditions, the stabilization point of the lifted flame moved downstream. b) at the critical liftoff condition, the flow rate of DME decreased with the increase of N2, while the total flow rate was almost unchanged, so the jet velocity was almost the same. c) as Z increased, the stabilization zone of the DME liftoff flames became narrow and small. In the experimental study of the effects of the nozzle diameter on the flame liftoff characteristics, six nozzles with i.d. of 0.17mm, 0.25mm, 0.386mm, 0.43mm, 0.693mm and 1.152mm were used. These nozzles had different materials and nozzle exit types. The experimental results showed that the nozzle inner diameter has a significant impact on the flame liftoff characteristics. As the nozzle diameter increased, four types of different liftoff features were observed. The flame was blown out directly with i.d. of 0.17 mm. The DME flame could only be observed liftoff by ignition at a proper position downstream with i.d. of 0.25 mm, 0.386 mm and 0.43 mm. The observations are agreed with that reported in the literatures. While it could be lifted off directly by increasing the mass flow rate of fuel/dilution with i.d. of 0.693 mm. This is the new observation in the present work. It is different from the report in the literatures that the DME flame could not be lifted off directly by increasing the jet velocity except for far field ignition at relatively low mass flow rate. When the nozzle i.d. was increased to 1.152 mm, the DME flames could be lifted off by three different methods: increasing the flow rate of fuel/dilution, decreasing the flow rate of the fuel and ignition the flame downstream. Oscillation lifted DME flames were found with i.d. of 1.152 mm when the fuel was highly diluted by nitrogen. The experimental results also showed that the critical liftoff velocity Ulo and the critical blowout velocity Ubo were strongly dependent on the inner diameter, which decreased with the increase of the nozzle diameter. When the jet velocity was kept constant, the flame liftoff height HL increased with the increase of the nitrogen mole fraction Z for all lifted flames.

The Effect of Nozzle Diameter on Jet Impact for a Tricone Bit

1984 ◽  
Vol 24 (01) ◽  
pp. 9-18 ◽  
Author(s):  
T.M. Warren ◽  
W.J. Winters
Keyword(s):  
Impact Force ◽  
Penetration Rate ◽  
Nozzle Diameter ◽  
Constant Weight ◽  
Jet Impact ◽  
Fluid Properties ◽  
Jet Energy ◽  
The Impact ◽  
Indiana Limestone ◽  
Hole Bottom

Abstract Conventional techniques used to optimize the hydraulic conditions run with tricone bits usually are aimed at maximizing either jet hydraulic horsepower or jet impact force. A basic assumption underlying these optimization methods is that increased energy at the nozzle produces increased energy at the bottom of the hole. Conventional tricone bit nozzles are aimed at the "corner" of the borehole. The jets exist in a crossflow due to the return path of the fluid from under the bit. Many studies document the deflection and diffusion of a submerged jet stream in a crossflow. Studies were conducted with an 8 1/2-in. [21.59-cm] Intl. Assn. of Drilling Contractors (IADC) Series 6–1-7 bit to determine the area and magnitude of the jet impact under a tricone bit. Flow rates up to 565 gal/min [35.6 dm /s] and jet velocities up to 400 ft/sec [122 m/s] were used. The impact area was determined by (1) observing the location of an eroded zone beneath the bit in a block of Indiana limestone and (2) measuring the dynamic pressure beneath the bit in a test cell. Both tests indicate that a larger fraction of the jet energy reaches the hole bottom with small jets than with large jets. The tests also indicate that a larger fraction of the jet energy reaches the hole bottom when two jets are used instead of three. Introduction Flow rate, fluid velocity, jet nozzle geometry and drilling fluid properties are well recognized as factors that affect the penetration rates of tricone bits. Parameters such as jet impact force, hydraulic horsepower, jet velocity, and jet Reynolds number have been used in attempts to quantify the effect of bit hydraulics on penetration rate. All these parameters refer to fluid properties at the nozzle. It is assumed that these parameters also reflect the hydraulic energy at the bottom of the hole. There is no consensus on which parameter most directly governs bit hydraulic effects on rate of penetration (ROP) or on the exact mechanism by which hydraulics affects penetration rate. The parameters most commonly used to quantify the effect of hydraulics on ROP are jet impact force and hydraulic horsepower per square inch of bit area. Given a maximum allowable surface pump horsepower, standpipe pressure, and drillstring geometry, there is a unique set of nozzles that maximize either hydraulic horsepower or jet impact force at the bit. Maximum horsepower is obtained with smaller nozzles than are required to maximize impact force. The optimal hydraulic condition usually is considered to be that which gives either maximum impact or horsepower at the bit while keeping the annular velocity within limits established by borehole erosion and cuttings transport considerations. It is assumed that the optimal nozzle diameter is the diameter required to maximize either bit hydraulic horsepower or impact force. This assumption is valid only if the horsepower or impact force equations completely account for the effect of nozzle diameter on bit cleaning, Over the years, laboratory test data obtained with the drilling rig described in Ref. 1 have indicated that ROP is a function of nozzle diameter at constant bit hydraulic horsepower conditions. The drilling rate tests reported here were conducted specifically to determine the influence of nozzle diameter on ROP. An 8 1/2-in. [21.59-cm] IADC Series 6–1-7 bit was used to drill Indiana limestone with a 9.1 -lbm/gal [1090-kg/m ] claybase mud. The tests were run with a constant weight on bit (WOB) of 42,000 lbf [187 kN], a rotary speed of 75 rpm [1.25 rev/s] and a borehole pressure of 100 psi [689 kPa]. Fig. 1 shows the results of these tests for nozzle diameters of 9/32 in. [0.71 cm], 13/32 in. [1.03 cm], and 15/32 in. [1.19 cm]. The figure clearly shows both a large effect of impact force and an influence of nozzle diameter independent of impact force on ROP. For example, 500 lbf [2.22 kN] of impact force with three 9/32 in. [0.71-cm] nozzles gives the same ROP as 800 lbf [3.56 kN] of impact with three 15/32-in. [1.19-cm] nozzles. A similar effect is observed when ROP is plotted vs. hydraulic horsepower. Rock erosion tests and pressure measurements beneath the bit were used to evaluate the cause of these differences. Literature Review The hydraulic environment under a conventional tricone bit is quite complicated. Several factors that are likely to affect the fluid flow and cuttings removal from under a bit are discussed in the following. The jets on the bit are aimed toward the corner of the borehole bottom with an inclination of 10 to 15 deg. as shown in Fig. 2. The flow field of the jet may be influenced by the wellbore wall, bottom of the hole, cones on the bit, and returning fluid from under the bit, as well as stagnation zones under the bit due to the effect of adjacent jets. The approach taken in this literature survey is to review the available information pertaining to each of these parameters individually. SPEJ P. 9^

scholarly journals A peculiar behaviour of liquid jet impact

2019 ◽  
Vol 85 ◽  
pp. 05001
Author(s):  
Claudiu Pătraşcu ◽  
Corneliu Bălan
Keyword(s):  
Reynolds Number ◽  
Flow Rate ◽  
Critical Reynolds Number ◽  
Bond Number ◽  
Critical Distance ◽  
Liquid Jet ◽  
Upper Limit ◽  
Peculiar Behaviour ◽  
Jet Impact

Coalescent masses of fluid, formed upon liquid jet impact, should exhibit either dripping or jetting regardless of the distance between the nozzles. The study reveals that above a certain flow rate, by increasing this distance, the coalescent mass enters a dripping state, when only a jetting regime is previously present. This is followed again by a jetting regime before breakup which occurs at a critical distance. The upper limit of this dripping state is achieved when Bond number is equal to unity, this result being valid below a certain critical Reynolds number.

THE INFLUENCE OF THE FLOW RATE ON THE JET IMPACT FORCE

2019 ◽  
Author(s):  
Jonatas Borges ◽  
Sammy Cristopher Paredes Puelles ◽  
Elie Luis Martínez Padilla ◽  
Marcos Lourenço
Keyword(s):  
Flow Rate ◽  
Impact Force ◽  
Jet Impact

Pressure Drop Measurements for Air Flow Through Open-Cell Aluminum Foam

2004 ◽  
Author(s):  
Nihad Dukhan ◽  
Angel Alvarez
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Flow Rate ◽  
Aluminum Foam ◽  
Flow Direction ◽  
The Other ◽  
Turbulent Regime ◽  
Thick Sample ◽  
Open Cell ◽  
Two Samples

Wind-tunnel pressure drop measurements for airflow through two samples of forty-pore-per-inch commercially available open-cell aluminum foam were undertaken. Each sample’s cross-sectional area perpendicular to the flow direction measured 10.16 cm by 24.13 cm. The thickness in the flow direction was 10.16 cm for one sample and 5.08 cm for the other. The flow rate ranged from 0.016 to 0.101 m3/s for the thick sample and from 0.025 to 0.134 m3/s for the other. The data were all in the fully turbulent regime. The pressure drop for both samples increased with increasing flow rate and followed a quadratic behavior. The permeability and the inertia coefficient showed some scatter with average values of 4.6 × 10−8 m2 and 2.9 × 10−8 m2, and 0.086 and 0.066 for the thick and the thin samples, respectively. The friction factor decayed with the Reynolds number and was weakly dependent on the Reynolds number for Reynolds number greater than 35.

scholarly journals Net-exergetic, hydraulic and thermal optimization of coaxial heat exchangers using fixed flow conditions instead of fixed flow rates

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Tobias Blanke ◽  
Markus Hagenkamp ◽  
Bernd Döring ◽  
Joachim Göttsche ◽  
Vitali Reger ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Mass Flow ◽  
Flow Rate ◽  
Heat Exchangers ◽  
Circular Ring ◽  
Flow Conditions ◽  
Flow Rates ◽  
Mass Flow Rates ◽  
Pipe Radius

AbstractPrevious studies optimized the dimensions of coaxial heat exchangers using constant mass flow rates as a boundary condition. They show a thermal optimal circular ring width of nearly zero. Hydraulically optimal is an inner to outer pipe radius ratio of 0.65 for turbulent and 0.68 for laminar flow types. In contrast, in this study, flow conditions in the circular ring are kept constant (a set of fixed Reynolds numbers) during optimization. This approach ensures fixed flow conditions and prevents inappropriately high or low mass flow rates. The optimization is carried out for three objectives: Maximum energy gain, minimum hydraulic effort and eventually optimum net-exergy balance. The optimization changes the inner pipe radius and mass flow rate but not the Reynolds number of the circular ring. The thermal calculations base on Hellström’s borehole resistance and the hydraulic optimization on individually calculated linear loss of head coefficients. Increasing the inner pipe radius results in decreased hydraulic losses in the inner pipe but increased losses in the circular ring. The net-exergy difference is a key performance indicator and combines thermal and hydraulic calculations. It is the difference between thermal exergy flux and hydraulic effort. The Reynolds number in the circular ring is instead of the mass flow rate constant during all optimizations. The result from a thermal perspective is an optimal width of the circular ring of nearly zero. The hydraulically optimal inner pipe radius is 54% of the outer pipe radius for laminar flow and 60% for turbulent flow scenarios. Net-exergetic optimization shows a predominant influence of hydraulic losses, especially for small temperature gains. The exact result depends on the earth’s thermal properties and the flow type. Conclusively, coaxial geothermal probes’ design should focus on the hydraulic optimum and take the thermal optimum as a secondary criterion due to the dominating hydraulics.

Experimental Investigation of Effect of Tip Coolant Ejection on Internal Flow Characteristics Within a Realistic Blade Coolant Channel

2013 ◽  
Author(s):  
Jian Pu ◽  
Zhaoqing Ke ◽  
Jianhua Wang ◽  
Lei Wang ◽  
Hongde You
Keyword(s):  
Experimental Investigation ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Turbine Blade ◽  
Flow Rate ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Flow Ratio ◽  
Lp Turbine ◽  
Mass Flow Ratio

This paper presents an experimental investigation on the characteristics of the fluid flow within an entire coolant channel of a low pressure (LP) turbine blade. The serpentine channel, which keeps realistic blade geometry, consists of three passes connected by a 180° sharp bend and a semi-round bend, 2 tip exits and 25 trailing edge exits. The mean velocity fields within several typical cross sections were captured using a particle image velocimetry (PIV) system. Pressure and flow rate at each exit were determined through the measurements of local static pressure and volume flow rate. To optimize the design of LP turbine blade coolant channels, the effect of tip ejection ratio (ER) from 180° sharp bend on the flow characteristics in the coolant channel were experimentally investigated at a series of inlet Reynolds numbers from 25,000 to 50,000. A complex flow pattern, which is different from the previous investigations conducted by a simplified square or rectangular two-pass U-channel, is exhibited from the PIV results. This experimental investigation indicated that: a) in the main flow direction, the regions of separation bubble and flow impingement increase in size with a decrease of the ER; b) the shape, intensity and position of the secondary vortices are changed by the ER; c) the mass flow ratio of each exit to inlet is not sensitive to the inlet Reynolds number; d) the increase of the ER reduces the mass flow ratio through each trailing edge exit to the extent of about 23–28% of the ER = 0 reference under the condition that the tip exit located at 180° bend is full open; e) the pressure drop through the entire coolant channel decreases with an increase in the ER and inlet Reynolds number, and a reduction about 35–40% of the non-dimensional pressure drop is observed at different inlet Reynolds numbers, under the condition that the tip exit located at 180° bend is full open.

Numerical Simulations of Resonant Heat Transfer Augmentation at Low Reynolds Numbers

2001 ◽  
Author(s):  
Miles Greiner ◽  
Paul F. Fischer ◽  
Henry Tufo
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Natural Frequency ◽  
Flow Rate ◽  
Low Reynolds Number ◽  
Reynolds Numbers ◽  
Spectral Element ◽  
Pumping Power ◽  
Number Systems ◽  
Low Reynolds

Abstract The effect of flow rate modulation on low Reynolds number heat transfer enhancement in a transversely grooved passage was numerically simulated using a two-dimensional spectral element technique. Simulations were performed at subcritical Reynolds numbers of Rem = 133 and 267, with 20% and 40% flow rate oscillations. The net pumping power required to modulate the flow was minimized as the forcing frequency approached the predicted natural frequency. However, mixing and heat transfer levels both increased as the natural frequency was approached. Oscillatory forcing in a grooved passage requires two orders of magnitude less pumping power than flat passage systems for the same heat transfer level. Hydrodynamic resonance appears to be an effective method of increasing heat transfer in low Reynolds number systems where pumping power is at a premium, such as micro heat transfer applications.

Thermal and Fluid Dynamic Behavior of a Horizontal Channel With Adiabatic Moving Lower Plate

2005 ◽  
Author(s):  
Assunta Andreozzi ◽  
Vincenzo Naso ◽  
Oronzio Manca
Keyword(s):  
Heat Flux ◽  
Reynolds Number ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Horizontal Channel ◽  
Lower Plate ◽  
Stationary Condition ◽  
Moving Plate ◽  
Plate Velocity

In this study a numerical investigation of mixed convection in air in horizontal parallel walled channels with moving lower plate is carried out. The moving lower plate has a constant velocity and it is adiabatic, whereas the upper one is heated at uniform heat flux. The effects of horizontal channel height, heat flux and moving plate velocity are analyzed. Results in terms of temperature and stream function fields are given and the mass flow rate per unit of length and divided by the dynamic viscosity is reported as a function of Reynolds number based on the moving plate velocity. For stationary condition of lower plate, a typical C–loop inside the horizontal channel is detected. Different flow motions are observed in the channel and the two reservoirs, depending on the heat flux values and the distance between the heated upper stationary plate and lower adiabatic moving plate. The dimensionless induced mass flow rate presents different increase between the Reynolds number lower or greater than 1000.

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