熱力學專業的留學生essay制定-Air Jet Experiment

 

Abstract

A plate with a spring gauge is placed at the Pitot tube probe and there is an entry called orifice and exit called nozzle for the air generated by a fan. The fan gives air flow which makes the pressure on the plate on the opposite direction of the gravity as a force. The force on the plate can be measured in this experiment or calculated from the theory. Additionally the nozzle forms a jet boundary which is variable by the height of the plate. It was observed that the nozzle gives larger diameter of the boundary as the height of the plate increases. The force calculated in the theoretical work is larger than observed in the experiment.帶有彈簧的儀表板被放置在皮托管探針和有一個入口孔和出口被稱為一個風扇產生的空氣噴嘴。風扇使空氣流使印版上的壓力對重力方向相反的力。盤子上的力可以被測量或計算出的理論。此外，噴嘴形成的射流邊界的板的高度可變的。據觀察，提出了大直徑噴嘴的邊界板的高度的增加。在理論計算的力大于在實驗中觀察到的。

 

The experimental problem and theory

The first experiment is to study the force of a plate impinged by an air jet. The second experiment is to study the formation of a round air jet by a nozzle, tested by a plate. 

 

The force applied on the fluid with a certain length of time period has the result to change the momentum of the fluid. In other words, the force has the effect as the velocity change of the fluid at its mass flow rate.

 

Methodology

The first experiment is to measure the force on the round plate by jet below, for different distances. 實驗和理論問題

第一個實驗是研究板由一個空氣射流沖擊力。第二個實驗是通過一個噴嘴研究圓形空氣射流形成，由板測試。

所施加的力在一定時間段的長度的流體具有結果來改變流體的動量。換句話說，力在其質量流量的流體的速度變化的影響。

 

The second experiment is to measure the effective area of a jet. In additional to the height of the plate is a variable, the radial distance is another one so that at large distance it will ultimately gives zero force.

 

The plate has a spring gauge so that the force on it can be measured. The plate can be placed above the nozzle and adjusted to different heights and redial distances. The pitot tube has a probe which connects the manometer. Fan gives air jet to the nozzle. 

 

In experiments results are collected in trials which are compared with theoretical calculations.

 

Results and Discussion

For the first experiment plate heights from 0 to 90 cm are measured with step size 10 cm. From 0 to 90 cm the force measured are 1200g, 1080g, 1060g and so forth, respectively. In other words from 20 cm up the force remained in 1060g. The fan gives a pressure as 25mm fluid level increase was observed.#p#分頁標題#e#

 

Pressure 

P = 784* 9.8 * 0.025*sin15

 

Velocity at the orifice  

v(d) = sqrt(2P/Rho(air))

 

Exit velocity

v(e) = v(d) * (70/25)^2 = 71.07

 

mass flow rate

Rate(m) = C(d)rho(air)v(e)A(e) = 0.6*1.21*v(e)*A(e)= 0.0253 kg/s

 

Air density used = 1.21 kg/m^3

 

Force on the plate can be derived as

F = rate(m)*v(e) = C(d)*rho(air)*v(e)^2*A(e) = 1.798 kg

 

This value is larger than the experiment observed, which is about 1.08, 1.06 kg.

 

For the second experiment heights from 0 to 80 cm with step size 10 cm are measured with each height has 8 trials in different distances from center to outskirt. The measured fluid levels in manometer give that for closer distance to the nozzle, the central pressure is larger than further distance to the nozzle (i.e. lower position vs. higher position). On the other hand the boundary of the nozzle is increased as the plate was moved to higher (further) position. In other words, to develop nozzle area it needs a certain distance as the basis.  

 

In experiment 2, the jet boundary can be approximated by average on the weighted sum of force at each height; weight is taken as the redial distance, hence

 

height weighted sum sum jet boundary

10 92 229 0.401747

20 108 169 0.639053

30 50 84 0.595238

40 90 75 1.2

50 93 57 1.631579

60 101 47 2.148936#p#分頁標題#e#

70 100.5 39.5 2.544304

80 87.5 34 2.573529

 

Figure 1: The force as a function of the plate height

 

 

Figure 2: The average diameter as a function of the plate height.

Conclusions

It was observed that the nozzle gives larger diameter of the boundary as the height of the plate increases. The force calculated in the theoretical work is larger than observed in the experiment.

 

Compressible Flow Experiment

Abstract

Experience significant changes in the density of the fluid behavior are described compressible flow. Magnetic flux density can be simplified for analysis of flow behavior by assuming a constant density does not change significantly. This leads to the theory of idealized incompressible fluid. As a result, in most cases, significant changes in the density and gas, liquid handling (especially for high sales) because the flow of large pressure changes that can handle these cases, you can fix you must be obtained when analyzing the compressible flow.

 

The experimental problem and theory

The rest of the gas at supersonic speed in order to facilitate the convergence of the gas duct and the branch line for the first time subsonically accelerated by adding to the speed of the supersonic expansion is very important. Therefore, the outlet nozzle is designed to achieve supersonic flow conduit is convergentdivergent. Throat Mach number, can not exceed 1, the mass flow rate decreases, the output pressure of the nozzle becomes constant. This is the breath of the nozzle flow. Or equal to the formation of shocks, output does not exceed the design pressure or flow and shock wave deceleration nozzle pressure ratio that is designed to work are formed.

 

Methodology

Experiment 1: Resolving the change in pressure and counterpressure

 (A) supply pressure valve and back pressure valve is fully opened, is all.

 (B) such that the pressure re-measured static pressure probe completely surprised.

 (C) by adjusting the pressure valve on the pressure 500 kPa, reading level

In order to measure;

 (D) to adjust the pressure to change again to a new pressure valve: back of the stage pressure rise

Again, the pressure is the same procedure until the supply pressure. At each step, reading the water of the slope of the level of the pressure.

 

Experiment 2: the axis of the nozzle, the measurement of static pressure variation along the flow#p#分頁標題#e#

In this experiment, the two must be made to the supply pressure P0. Each supply pressure

It must re-establish the pressure of your number. Some results of the election to cover the back

Regimes: (A) through the speed of sound, (B) Sonic subsonic ? (neck) supersonic subsonic shock 

O (C) Sonic (design conditions) subsonic procedures in place at each step, reading the water level is the same as in Experiment 1, through exploration and reading the pressure at the nozzle through the nozzle gauge metric.

Results and Discussion

 

By adding a column to promote the cause of the fluid flowing through pipe sales in subsonic flow, it takes some time to add a column to a supersonic flow of a pipe flow. Zoning changes will make the flow of friction choking Mach number required to reach the column, similar to the above case will be added later.

 

For the ideal gas constant area of the pipe, the pipeline was held at Mach number of non-identical effects of changes in temperature is due to explain how you can use to calculate the Rayleigh flow model. Fixed temperature when the isentropic depression if it is delayed, in making liquid is the temperature. Increasing the temperature of the heat, such as congestion, added to the system.

 

Variation of mass flow rate with back pressure

back pressure Pb manometer water levels in inches p1-p2 mass flow rate

0 1.9 435.61 0.000351

50 1.9 435.61 0.000351

100 1.9 435.61 0.000351

150 1.85 423.164 0.000346

200 1.9 435.61 0.000351

250 1.9 435.61 0.000351

300 #p#分頁標題#e#1.9 435.61 0.000351

350 1.85 423.164 0.000346

400 1.6 360.934 0.00032

450 0.85 174.244 0.000222

500 -0.1 N/A N/A

 

And additional variables are available given the changes in the density analysis. Generally, conservation of mass conservation equation for incompressible flow can be resolved by considering, as opposed to. In general, includes the principle of conservation of energy. However, this is another variable (temperature), and the fourth equation, therefore, to describe the thermodynamic temperature of the flow that is required (e.g., ideal gas equation of state, etc.) has been introduced.

 

The identity politics of the density of the fluid density isentropic you, ρ0, the reference value, when you define a way to compress the stream can are stopped if that helps you compare the density. In principle, the static density is 5% or more relative to the change in density, must be analyzed and then compress the fluid flow. Ideal gas specific heat at a rate of 1.4 cases around the Mach number is greater than 0.3 occur. Below this value, however, in certain cases, may depend heavily compressed or the level of accuracy required, should be treated likely.

 

T = 473(1/5)^(1-1/1.2) = 361.7K

delta(s)/R = ln(p1/p2)(t2/t1)^(gamma/(gamma-1))

delta(s)/R = ln5(361.7/472)^3.5 = 0.671

delta(s) = 192.5J/Kg*K

 

p2 = p1+ delta(p) = 125kPa

p2/p1 = (Ma^2(gamma-1)/2+1)^(gamma/(gamma-1))=125/105

Ma = 0.634

a=rRT^0.5 = (1.4*287*294.7)^0.5 = 343

u = 217.7 = a*Ma

 

a1 = sqrt(rRT) = sqrt(1.3*188.95*300) = 271.46

 

T2/T1 = (1+(gamma-1)*M1^2)/2)/(1+(gamma-1)*M2^2)/2)

T2 = 399

u2 = a2*M2 = 201

 

Theoretical computation of the maximum mass flow rate

A(throat) = 3.14159*0.00479^2/4 = 1.80202E-05

M(max) = A(throat)*(1.21*287*294.4*1.21*1.4*(5/6)^6)^0.5 = 0.004339863#p#分頁標題#e#

 

Conclusions

One of the most common examples of shock waves of compressible flow phenomena. Impact on the thermodynamic properties is characterized by discontinuous change. Pressure wave is suddenly removed from the series together to form a membrane separating two different regions of compression or shock-dimensional flow. This is a technique used to generate shock waves in shock tube is often. Compressible fluid nozzle has an important role in determining behavior. Subsonic and supersonic flows react differently to changes in cross section. Convergence of the duct (small diameter, large diameter in the direction of flow reduction) is increased through experience, the speed of subsonic flow, supersonic flow by reducing the speed of the train, making the production. In general, the flow through a convergent nozzle, the Mach 1 always tends to be. Convergence is large enough to reach the speed of sound, known as the place "choking" phenomenon. In this case, the flow of shortness of breath, and the two tubes at once, speed limits, number of shock Mach entering the fluid flow area or at least (and units like this is known as a sore throat maintenance, etc.), type of nozzle. Similarly, the difference between slow flow is always subsonic flow through a nozzle, and is supersonic.一個可壓縮流動現象的沖擊波最常見的例子，熱力學性質的影響具有不連續的變化。壓力波是突然從系列一起拆下形成的膜分離兩個不同區域的壓縮或沖擊的三維流動。這是一個用激波管產生的沖擊波技術往往是。可壓縮流體噴嘴具有重要作用，在確定的行為。亞音速和超音速流動的橫截面的變化有不同的反應。（小直徑的管匯合，在流量減少的方向大直徑）是通過增加經驗，亞音速超音速流的速度，減少了列車的速度，使生產。在一般情況下，通過一個收斂噴管流動，馬赫1很容易。收斂是大到足以達到聲音的速度，稱為“Choking”現象。在這種情況下，呼吸急促的流量，和兩個管一次，速度限制，激波馬赫進入流體流動區域或至少數（單位一樣，這稱為喉嚨痛的維護，等），式噴嘴。同樣，在緩慢流動的差異始終是亞音速流通過一個噴嘴，并是超音速的。