Pressure distribution on an ellipto-zhukovsky aerofoil Essay Example

Pressure distribution on an ellipto-zhukovsky aerofoil Paper The pressure distribution around an Ellipto Zhukovsky aerofoil with a chord of 254 mm at a range of angles of attack (-4? , 7? and 15? ) was determined and pressure contributions to lift were evaluated in a T3 wind tunnel at City University. This was carried out at a chord Reynolds number of 3. 9 x 105. Graphs for lift and pitching moment coefficients were plotted against angles of attack. A graph for Cm and Cl was also plotted from which the aerodynamic centre was determined to be 23. 7%. The value of lift curve slope was determined to be 4. 4759. Hence the value of k (the ratio of the actual lift curve slope to the theoretical one) for this aerofoil was determined to be 0. 917. The value of Cmo was also found to be 0. 0172. Specimen calculations for 15 degrees angle of attack can be found in the appendix section. LIST OF SYMBOLS Cp Pressure Coefficient Cpu Pressure Coefficient of upper surface Cpl Pressure Coefficient of lower surface Cl Lift Coefficient Cm Moment Coefficient x/c Position of pressure tapping on aerofoil divided by chord length Px Pressure at tapping x (Pa) Patm Atmospheric Pressure (Pa) ? Density of air (kg/m3) i Dynamic viscosity ? Kinematics viscosity (m/s2) We will write a custom essay sample on Pressure distribution on an ellipto-zhukovsky aerofoil specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Pressure distribution on an ellipto-zhukovsky aerofoil specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Pressure distribution on an ellipto-zhukovsky aerofoil specifically for you FOR ONLY $16.38 $13.9/page Hire Writer h Digital manometer reading ? angle of which manometer is inclined D or t Diameter of cylinder (mm) h tunnel height (mm) V Velocity of air flow (m/s) R Molar gas constant (J/kg. K) T Temperature (K) Re Reynolds Number INTRODUCTION An airfoil is any part of an airplane that is designed to produce lift. Those parts of the airplane specifically designed to produce lift include the wing and the tail surface. In modern aircraft, the designers usually provide an airfoil shape to even the fuselage. A fuselage may not produce much lift, and this lift may not be produced until the aircraft is flying relatively fast, but every bit of lift helps. The first successful aerofoil theory was developed by Zhukov sky and was based on transforming a circle onto an aerofoil-shaped contour. This transformation gave a cusped trailing edge, and so the transformation was modified to obtain a slender semi-eclipse trailing edge, which gave rise to the name Ellipto Zhukovsky. When a stream of air flows past an aerofoil, there are local changes in velocity around the aerofoil, and consequently changes in static pressure in accordance with Bernoullis theorem. The distribution of pressure determines the lift, pitching moment, form drag, and centre of pressure of the aerofoil. In our experiment we are concerned with the effect of pressure distribution on lift, pitching moment coefficient (Cm), and centre of pressure. The centre of pressure can be defined as the point on the aerofoil where Cm is zero, and therefore the aerodynamic effects at that point may be represented by the lift and drag alone. A positive pressure coefficient implies a pressure greater than the free stream value, and a negative pressure coefficient implies a pressure less than the free stream value (and is often referred to as suction). Also, at the stagnation point, Cp has its maximum value of 1 (which can be observed by plotting Cp against x/c). Zhucovsky claimed that the aerofoil generates sufficient circulation to depress the rear stagnation point from its position, in the absence of circulation, down to the (sharp) trailing edge. There is sufficient evidence of a physical nature to justify this hypothesis and the following brief description of the Experiment on an aerofoil may serve helpful. The experiment focuses on the pressure distribution around the Zhucovsky airfoil at a low speed and the characteristics associated with an airfoil:  coefficient of lift,   coefficient of pitching moment   and centre of pressure. The airfoil is secured to both sides of the wind tunnel with pressure tappings made as small as possible not to affect the flow,(appendix- photo 1 . The pressure difference around the airfoil is measured with twenty-five manometer readings which are recorded for each angle of attack. The manometer fluid is alcohol and has a specific gravity of 0. 83 and inclined at an angle of 30 degrees. Tube 1 is left open to atmospheric pressure, while tubes 2-13 are the lower surface of the airfoil and tubes 14-24 are the upper surface of the airfoil. The pressure tapings are positioned on the airfoil at a distance x/c, noted in the results table and tube 35 is the static pressure of the wind tunnel. The dynamic pressure is given by a digital manometer. The digital readout results were used for all calculations because they are more precise. Results Raw data and calculated values for x/c, Cp and Cp(x/c) can be found in the appendix. Graphs of Cp against x/c for angles of attack -4, 7, and 15 degrees can be also be found in the appendix. These graphs determine the lift coefficient. Counting the squares method was used to determine the values of Cl. Graphs of Cp*(x/c) against x/c for angles of attack -4, 7, and 15 degrees can be also be found in the appendix. These graphs determine the pitch moment coefficient. Counting the squares method was used to determine the values of Cm. Graphs of Cl against angle of attack ,Cm against angle of attack, and Cm against Cl can be found in the appendix. Also below is a summary of the results: Angle of Attack (degrees) Cl Cm -4 -0. 513 0. 153 7 0. 740 -0. 166 15 0. 946 -0. 183 Discussion The experiment was conducted in a low speed, closed wind tunnel, operating at approximately 50% of its speed. The aerofoil was mounted in the wind tunnel and its pressure tapings connected to a manometer inclined at 30 degrees to the horizontal. The height of the liquid in each manometer tube represented the pressure acting on each of the aerofoil tapings. The pressure in the working section, and the pressure at the venturi inlet were taken into account, and a resulting wind tunnel velocity was displayed on a digital manometer. The Reynolds number was calculated (see appendix. Values of Cl and Cm for other angles of attack were obtained from other groups conducting the experiment, and were used to obtain more accurate graphs. It was also found that the slope of the Cl against angle of attack graph was 4. 4759, which was not relatively close to the theoretical value of 7. 105. The aerodynamic centre was calculated at 23. 7% of the chord length (from the slope of the Cm against Cl graph). It was found that the lift increased with angle of attack, up to a point where the aerofoil experiences stall, and a dramatic loss of lift occurs. As there was little change in the lower surface pressure distribution, the lift was mainly generated due to the upper surface suction. As the angle of attack increases, the height of the upper surface suction peak should increase, and move forward, indicating that the centre of pressure is moving forward. However, experimentally this was not prominent, and can be attributed to a possible disturbance in the pressure distribution around the aerofoil. At zero degrees angle of attack, for a symmetrical aerofoil, lift and Cm should equal zero. The reason that they were not zero means that the aerofoil must have had a very small angle of attack. The discrepancy between the theoretical and experimental value of lift curve slope is due to boundary layer effects, and the effect of the thickness of the aerofoil, and thus the theoretical value needs to be multiplied by the k value (=0. 917) to obtain the experimental result. Conclusion The aim of the experiment was achieved with a relatively good level of experimental accuracy. The pressure distribution over an aerofoil contributes towards the lift and pitching moment coefficient, where the increase in suction on the upper surface (due to an increased angle of attack) increases the lift, and pitching moment coefficient. The variation of pressure distribution also affects the location of the centre of pressure. The factors which affected the pressure distribution, were mainly the thickness and the Reynolds number. However, when it comes to comparing the results with their theoretical values it is clear to see that there have been significant errors have occurred in the experiment. These are listed below. Human errors in reading of the manometer tubes. Where several people were involved and this led to different techniques being used it would have been best for everyone to take their own set of readings and the average value calculated using all the data. The most common error without ant doubt was parallax and this could have been avoided by using digital measuring devices. Calculation errors i. e. rounding off, conversion error and error occurring when the area under the graphs was calculated for the coefficient of lift.   Experimental errors some of the tapping may have been defective and not enough tapping were provided. Also to obtain a better lift curve slope there should have more angles of attack. Also any obstructions in front of the wind tunnel such as people would create unnecessary turbulence inside the wind tunnel. Appendix Specimen Calculations.

How is the Theme of Relationships explored in Gillian Clarkes Catrin, another Clarke Poem and Two Heaney Poems Essays

How is the Theme of Relationships explored in Gillian Clarkes Catrin, another Clarke Poem and Two Heaney Poems Essays How is the Theme of Relationships explored in Gillian Clarkes Catrin, another Clarke Poem and Two Heaney Poems Paper How is the Theme of Relationships explored in Gillian Clarkes Catrin, another Clarke Poem and Two Heaney Poems Paper Essay Topic: Literature Relationships can be portrayed through biological links, friendships and bonds between subjects of connotations and meaning. The intention of both poets is mainly to portray the strengths and weaknesses behind all bonds and the effect they encompass on the reader. Poets have the power to create, transform and enlighten upon a subject that may seem appropriate, but a relation amid love and hate can neither create nor destroy; the power of emotion will never subside through poetry. The exploration of Clarke and Heaneys poems will later be discovered when travelling the rendered emotions of Catrin, Baby-sitting, Follower and Death of a Naturalist. The mentioned poets use their personal experiences and perform the meaning of them using a conversion of techniques and influences. This is to enhance the importance to the reader of the purpose of the poem. Amongst the stated poems, the theme of biological and non-biological relationships can be declared as a core factor for the strength and duration of a bond. Clarkes Catrin is structured as an image of a tug-of-war between mother and baby, whilst resembling the struggle of the love for one another and what binds mother and baby together. The tight/ Red rope of love which we both fought over foreshadows this idea. The depth of explanatory vision can be seen as the umbilical cord which is later cut at birth creating an image of separation and division alongside the child becoming independent. All mothers face times when separation would benefit their child, but the safety and dangers that may be confronted, form a barrier for this dependency. The struggle faced in this maternal relationship, hold powerful emotions and deep-felt feelings From the hearts pool. The poem introduces a personal quality with the title Catrin but is then not mentioned again throughout the poem. This can be represented as a very personal relationship that does not have the need to direct but contain an unmentioned bond. However it could also resemble a relationship between any particular mother and child, giving the poem a sense of universality. The language used is simple and recognisable, which indicates the simple sincere emotions that are intended to be conveyed through the poem. The poems structure is two unbalanced stanzas, both performed in the past and present; an emphasis of how the relationship is still as intense from birth. A similar relationship based on a father: son bond is Heaneys Follower where Heaney both literally and metaphorically followed his father. The basic six stanza poem represent a clear division between father and son; three stanzas each. Heaney states how he imitates his father, following in his fathers footsteps, enhancing the biological bond and respect Heaney has for his father. Also, throughout the poem, the correct agricultural language can be found, highlighting the need Heaney felt to praise his father with respect as well as knowledge of his profession, and the future Heaney longed to pursue. The mother and child maternal bond can be perceived in Clarkes poem, Baby-sitting. Here, a non-biological bond of the strengths and adoration of a natural mother and child bond is shown to be instinctive between the characters but has occurred naturally and the anxiety Clarke feels towards another child she does not know. To be enchanted by your own babys breathe is a natural and maternal sentiment however, Clarke describes that there will be no chemistry or familiarity between them. The finality of this poem can be seen as indefinite for it suggests both literally that no milk will come but also a metaphor of how the motherly milk-familiar comforting, the connection will not come therefore she cannot totally provide for the child. The feeling of adoration between relations, friendships and subjects is described through many of the Clarke and Heaney poems studied. In Heaneys poem Follower, utter adoration and admiration is portrayed through Heaneys ability to use correct agricultural lexis of ploughing terms such as wing and sock. Heaney describes how both literally and metaphorically he followed his father. Heaney states he recalls his admiration for his father and using contrast to note how the young Heaney wanted to grow up and plough. To compare, Heaneys Death of a Naturalist represents his attitudes to the natural world in his childhood and his interest and appreciation towards nature, enhancing a passion inside him yearning for a great future. He receives encouragement from his teacher supporting and educating him on the subject of nature which he so fondly adores. Therefore in return he gives Miss Walls respect and esteem whilst quoting her on the knowledge learnt. Heaney wrote this poem with confidence, explaining with knowledge the process of how he took the frogspawn, placed them in jam pots and observed nature taking its toll. By using vocabulary to describe the pleasant as well as objectionable things such as festered, rotted, slobber, and slime kings shows young Heaney felt comfortable seeing nature close up, but perhaps he didnt fully understand the flaws in nature, as referring to reproduction focused on the mammy and daddy frog. Heaney accounts for his adventurous, inspirational but flawed childhood; this is in contrast to Clarkes more motherly approach to her somewhat misfortunate adulthood. Her Baby-sitting account resembles how her maternal relationship with the child is much stronger than any other could be. Even though to some extent the mentioned child disgusts her, Clarke introduces qualities that depict an ideal infant as pretty and appealing, roseate and bubbling and fair. However, she uses a statement foreshadowing quite a selfish outlook and to some degree insulting, when depicting the child of a perfectly acceptable child. Clarkes poem has no obvious metre, using short lines and limited use of metaphors and stresses. Baby-sitting can be seen to portray a specific event which anyone can relate to, but to explore a key difference between a motherly concern for another and a powerful, instinctive reaction to an unfamiliar happening. A relationship can be strong and well-built on a connection or a familiar bond correlating between the two. A relationship may last only for a moment, days, months, years or even last a life-time. Nevertheless, to become separate is to become distant from one another and through these poems, it can be found as a tangible bond that must be cut a tight red rope of love, or just be by age or differences which divide the two. Throughout Catrin, the struggle of separation, to be two is seen flowing fluid through each line however; there is no cause for the separation. Through birth and through time, the mother and child fight over the tight red rope if love and still, to prevent the distance between the two ever causing complete partition, she states she still fights, for the love is still as intense from birth. Within the poem, oddments of independence begin, but the old rope will surely keep them safe. However, a relationship may never truly fortify as neither one nor the other will love. Clarkes Baby-sitting explores an event that could belong to anyone. It depicts a strong need for replacement or a substitute, which can cause grief and a failure to enchantment. The opening of the poem explicates simply of the situation, however describing the baby as wrong. The baby can surely not be blamed but for Clarkes immediate assumptions, she fears what will shortly awake. She is scared to be hated by this child, to fear the hot midnight rage. The babys running nose will disgust her and the babys perfume of breath is purely a comparison against her own babys breath, whose does enchant her. The second stanza introduces the thought of abandonment. However, this separation, this desertion or rejection of the baby is depicted as far worse than that of the lover cold in lonely sheet. The baby will expect milk-familiar comforting but she will not find it. The love and interest for something, the power of a passion inside of you should never really die, but when obstructions hit or a barrier stops you from your dream, to grow apart from it may seem the only way. Heaney depicts his childhood adoration of nature in Death of a Naturalist, with a longer first stanza informing the reader upon his adventures and interest and knowledge on the seasonal process of frogs. Every spring Heaney would fill jampotfuls of his devotion to nature, only to find an experience of growing up to end this fantasy. Heaney hits realisation of growing up to feel threatened by nature, to not have power over its beauty and the feeling of his passion dying, to have to compromise and never fulfil his dream. The shorter second stanza creates a semantic field of war with expressions of anger, invasion, aggression, violence, rage, vengeance and mud grenades. Heaney feels rejected by something he once loved; he was invaded by something threatening and unfamiliar. He lost his passion in nature. Overall relationships can be discovered in all of the stated poems. The main theme mentioned is the maternal bond between parent and child. This is specifically highlighted in Catrin, in which the maternal bond remains strong and sturdy. However this bond is deemed to have been broken at birth, by the cutting of the umbilical cord, but this is only the physical bond, whereas the emotional bond will remain between the two forever.