ﺔﺴﺍﺭﺩ ﻊﻤ ﻁﺴﺒﻨﻤ ﺢﻁﺴ ﻰﻠﻋ ﻁﺎﻐﻀﻨﻼﻟ لﺒﺎﻗ ﻕﻓﺩ
ﺓﺭﺍﺭﺤﻟﺍ ﺔﺠﺭﺩ ﻲﻓ ﺩﺎﺤ ﺭﻴﻐﺘ
ﻲﻨﺍﺭﻫﺯﻟﺍ ﻪﻴﻁﻋ ﻱﺯﺎﻏ ﺩﻤﺤﻤ
ﺹﻠﺨﺘﺴﻤﻟﺍ
ﺀﺍﻭﻬﻟﺍ ﺎﻜﻴﻤﺎﻨﻴﺩ ﻥﻋ ﺔﺠﺘﺎﻨﻟﺍ ﺔﻴﺭﺍﺭﺤﻟﺍ لﺎﻤﺤﻷﺍ ﺔﻠﻜﺸﻤ ﺔﺴﺍﺭﺩ ،ﺙﺤﺒﻟﺍ ﻩﺫﻫ ﻲﻓ ﷲﺍ ﺩﻤﺤﺒ ﻡﺘ ﺎﻘﻴﺒﻁﺘ ﻊﻤ ﺔﻴﻠﻴﺼﻔﺘ ﺔﺴﺍﺭﺩ ﺀﺍﻭﻬﻟﺍ ﺎﻜﻴﻤﺎﻨﻴﺩ ﺕﺎﺒﺎﺴﺤ ﻡﺍﺩﺨﺘﺴﺎﺒ ﺕ
(CFD)
.
ﺡﺭﺸﻟﺍ ﻠﻴﺼﻔﺘﻟﺍ
ﻲ
ﻟ ﺔﻴﻠﻴﻠﺤﺘﻟﺍ ﺔﻴﺭﻅﻨﻠﻟ ﺔﻟﺄﺴﻤ
ﻲﺘﻭﺼ ﻕﻭﻓ ﻕﻓﺩﻟ ﻁﺴﺒﻨﻤ ﺢﻁﺴ ﻰﻠﻋ ﺓﺭﺍﺭﺤﻟﺍ ﺔﺠﺭﺩ ﻲﻓ ﺩﺎﺤﻟﺍ ﺭﻴﻐﺘﻟﺍ
ﹰﺎﻴﺒﻴﺭﺠﺘ ﺔﻨﻜﻤﻤﻟﺍ ﻁﻭﺭﺸﻠﻟ ﺕﺎﻘﻴﺒﻁﺘ ﻊﻤ ﺕﻤﺩﻗ .
ﺔﺠﺘﺎﻨﻟﺍ ﺔﻴﺌﺎﻴﺯﻴﻔﻟﺍ ﺭﻫﺍﻭﻅﻟﺍ لﻜ ﺽﺭﻋ ﻡﺘ ﻙﻟﺫﻜ
ﺤﻤﻟﺍ ﺓﺭﺍﺭﺤﻟﺍ لﺎﻘﺘﻨﺍ ﻭ ﻁﻐﻀﻟﺍ ﺭﻴﻐﺘ ﻥﻤ ﺓﺭﺍﺭﺤﻟﺍ ﺔﺠﺭﺩ ﻲﻓ ﺩﺎﺤﻟﺍ ﺭﻴﻐﺘﻟﺍ ﺓﻭﻁﺴﻟ ﺏﺤﺎﺼﻤﻟﺍ ﺔﻴﻠ
.
ﻊﻤ ﺔﻘﻘﺤﻤﻟﺍ ﺕﺎﻨﺭﺎﻘﻤﻟﺍ ﺞﺌﺎﺘﻨ
ﺕﻁﻋﺃ ،
CFDًﹰﺎﻘﻓﺍﻭﺘ ﺞﺌﺎﺘﻨﻟﺍ ﻊﻤ ﹰﺍﺩﻴﺠ لﻭﻠﺤﻟﺍ ﻥﻤ ﺔﻁﺒﻨﺘﺴﻤﻟﺍ
ﺔﻟﺄﺴﻤﻠﻟ ﺔﻴﺭﻅﻨﻟﺍ .
لﻤﺎﻜﻟﺍ ﺩﺍﺩﻋﻹﺍ ﻊﻤ ﻪﺘﻴﻟﺎﻌﻓ ﺕﺎﺒﺜﺇ ﻭ ﺔﺒﺭﺠﺘﻟﺍ ﺝﺫﻭﻤﻨ ﻡﻴﻤﺼﺘ ﻙﻟﺫ ﺩﻌﺒ ﻡﺘ ﺩﻘﻟ
ﺍ ﻲﻓ ﺕﺎﺤﺎﺠﻨﻟﺍ ﺭﺒﻜﺍ ﻥﻤ ﺩﻌﻴ ﻙﻟﺫ ﻭ ﺔﺒﺭﺠﺘﻠﻟ ﺙﺤﺒﻟ
.
ﻲﺌﺍﻭﻬﻟﺍ ﻕﻔﻨﻟﺍ ﻲﻓ ﺏﺭﺎﺠﺘﻟﺍ ﺕﻴﺩُﺃ
KAU-AT0ﺔﻟﺄﺴﻤ ﻲﻓ ﻕﻴﻘﺤﺘﻠﻟ ﺯﻴﺯﻌﻟﺍﺩﺒﻋ ﻙﻠﻤﻟﺍ ﺔﻌﻤﺎﺠﺒ
ﺓﺭﺍﺭﺤﻟﺍ ﺔﺠﺭﺩ ﻲﻓ ﺩﺎﺤ ﺭﻴﻐﺘ ﻊﻤ ﻁﺴﺒﻨﻤ ﺢﻁﺴ ﻰﻠﻋ ﻁﺎﻐﻀﻨﻺﻟ لﺒﺎﻘﻟﺍ ﻕﻓﺩﻟﺍ .
ﺕﺎﺒﻭﻌﺼﻠﻟ ﹰﺍﺭﻅﻨ
ﻡﺴﺠ لﻜﺸ ﻰﻠﻋ ﺭﺨﺁ ﺝﺫﻭﻤﻨ ﻡﻴﻤﺼﺘ ﺓﺩﺎﻋﺇ ﻡﺘ ،ﻁﺴﺒﻨﻤﻟﺍ ﺢﻁﺴﻟﺍ ﺝﺫﻭﻤﻨ ﺕﺍﺭﺎﺒﺘﺨﺇ ﺕﻬﺠﺍﻭ ﻲﺘﻟﺍ ﺯﻬﺠﻤ ﺭﻅﺎﻨﺘﻤ لﻴﺜﻤﻜ ﺝﺫﻭﻤﻨﻟﺍ لﻭﻁ ﻰﻠﻋ ﻕﻓﺩﻟﺍ ﻥﺎﻴﺭﺴ ﺩﺎﻤﺘﻋﺍ ﻡﺘ ﻭ ﺱﺎﻴﻘﻟﺍ ﺕﺍﻭﺩﺍ ﻊﻴﻤﺠﺒ
ﻁﺴﺒﻨﻤ ﺢﻁﺴ ﻰﻠﻋ ﻪﻨﺎﻴﺭﺴﻟ .
ﺕﺎﺴﺎﻴﻗ ﻊﻤ ﻥﻤﺍﺯﺘﻟﺎﺒ ﺓﺭﺍﺭﺤﻟﺍ ﻕﻓﺩﺘ ﺕﺎﺴﺎﻴﻗ لﻜ ﺝﺫﻭﻤﻨﻟﺍ ﻰﻠﻋ ﻡﺘ
لﺍ ﻡﺍﺩﺨﺘﺴﺎﺒ ﺓﺭﺍﺭﺤﻟﺍ ﺔﺠﺭﺩ ﻲﻓ ﺩﺎﺤﻟﺍ ﺭﻴﻐﺘﻟﺍ ﺔﻘﻁﻨﻤ لﻭﺤ ﺔﻋﺭﺴﻟﺍ .
PIV
ﺕﺎﻴﺩﺤﺘﻟﺍ ﺩﺤﺃ ﺭﻴﺼﻗ ﺔﺒﺭﺠﺘ ﻥﻤﺯ ﻲﻓ ﺓﺭﺍﺭﺤﻟﺍ ﻕﻓﺩﺘ ﺱﺎﻴﻗ ﺡﺭﺸ ﺽﺭﻋ ﻊﻤ ﺎﻬﺘﺴﺍﺭﺩ ﻡﺘ ﻲﺘﻟﺍ
لﺎﺠﻤﻟﺍ ﺍﺫﻫ ﻲﻓ ﺔﻤﺩﺨﺘﺴﻤﻟﺍ ﻕﺭﻁﻠﻟ .
ﺔﻴﻨﻘﺘ
Cook-Feldermanﺩﺤﺃ ﺓﺭﺍﺭﺤﻟﺍ ﻕﻓﺩﺘ ﺱﺎﻴﻗ ﻲﻓ
ﻡﻴﻗ ﺏﻠﻁﺘﺘ ﻻ ﺎﻬﻨﻭﻜ ﺎﻫﺭﺎﻴﺘﺨﺍ ﻡﺘ ﺩﻗ ﻭ ﺭﻴﺼﻘﻟﺍ ﻥﻤﺯﻟﺍ ﺕﺍﺫ ﺔﻴﺌﺍﻭﻬﻟﺍ ﻕﺎﻔﻨﻷﺍ ﻲﻓ ﺔﻌﺌﺎﺸﻟﺍ ﻕﺭﻁﻟﺍ ﺔﻴﺌﺩﺒﻤ ﺔﻴﻌﻗﻭﺘ .
لﺍ ﺕﺎﻴﻨﻘﺘ ﻲﻓ ﺕﺍﺭﻭﻁﺘﻟﺍ ﺭﺨﺁ )
(
PIVﻤﻌﻤ ﻲﻓ ﺎﻬﺒﻴﺼﻨﺘ ﻡﺘ ﺯﻴﺯﻌﻟﺍﺩﺒﻋ ﻙﻠﻤﻟﺍ ﺔﻌﻤﺎﺠ ﻕﻔﻨ ل
ﻲﺘﻭﺼ ﻕﻭﻓ ﻲﺌﺍﻭﻬﻟﺍ
KAU-AT0. ﻥﻤ ﻕﻘﺤﺘﻟﺍ ﻡﺘ ﺙﺤﺒﻟﺍ ﺍﺫﻫ ﻲﻓ ﺔﻴﻨﻘﺘﻟﺍ ﻡﺍﺩﺨﺘﺴﺍ لﺒﻗ
ﺎﻬﺘﺎﻴﻨﺎﻜﻤﺇ ﻡﺴﺠ لﻭﺤ ﺔﻋﺭﺴﻟﺍ ﺕﺎﻬﺠﺘﻤ ﺱﺎﻴﻗ ﻕﻴﺭﻁ ﻥﻋ ﺔﻴﺭﺍﺩﺠﻟﺍ ﺔﻘﺒﻁﻟﺍ ﻙﻤﺴ ﺱﺎﻴﻗ ﻲﻓ
ﺩﻨﻋ ﺭﻅﺎﻨﺘﻤ
2x107لﺍ ﺞﺌﺎﺘﻨ ﻊﻤ ﺩﻴﺠ ﻕﺒﺎﻁﺘ ﻲﻓ ﺔﺠﻴﺘﻨﻟﺍ ﺕﻨﺎﻜ ﺩﻗ ﻭ ،ﺯﻟﻭﻨﻴﺭ ﺩﺩﻋ .
CFD
ﻏﺭ ﺭﻴﻐﺘﻟﺍ ﻥﺃ ﻡ ﺞﺘﺎﻨﻟﺍ
ﹰﺎﻔﻴﻌﻀ ﻥﺎﻜ ﺓﺭﺍﺭﺤﻟﺍ ﺔﺠﺭﺩ ﻲﻓ ﺩﺎﺤ ﺭﻴﻐﺘﻜ ﻥﻴﺨﺴﺘﻟﺍ ﺔﻴﻠﻤﻋ ﻥﻤ )
step 17
T K
∆ =
( ﺓﺭﺍﺭﺤﻟﺍ ﺔﺠﺭﺩ ﻲﻓ ﺩﺎﺤﻟﺍ ﺭﻴﻐﺘﻟﺍ ﺕﺍﺭﻴﺜﺄﺘ ﺔﻴﺭﻅﻨ ﻥﻤ ﻕﻘﺤﺘﻠﻟ ﹰﺎﻴﻓﺎﻜ ﻥﺎﻜ ﻪﻨﻜﻟ ،
ﻕﻓﺩ ﺕﺎﺴﺎﻴﻗ ﻰﻠﻋ ﺓﺭﺍﺭﺤﻟﺍ
. ﻭﻴ ﺎﻤﻤ ﺓﺭﺍﺭﺤﻟﺍ ﺔﺠﺭﺩ ﻲﻓ ﺩﺎﺤﻟﺍ ﺭﻴﻐﺘﻟﺍ ﺭﻴﺜﺄﺘ ﺞﺌﺎﺘﻨﻟﺍ ﻩﺫﻫ ﺕﺒﺜﺃ ﺩﻟ
ﺔﻴﺭﺍﺭﺤﻟﺍ ﺔﻤﻅﻨﻻﺍ ﻡﻴﻤﺼﺘ ﺩﻨﻋ ﺭﺎﺒﺘﻋﻹﺍ ﻥﻴﻌﺒ ﻩﺫﺨﺃ ﻲﻐﺒﻨﻴ ﻱﺫﻟﺍ ﻭ ﻱﺭﺍﺭﺤﻟﺍ ﻕﻓﺩﺘﻟﺍ ﻲﻓ ﻥﺎﺸﻴﺠ .
ﻱﺩﺩﻌﻟﺍ لﻴﻠﺤﺘﻟﺍ ﺞﺌﺎﺘﻨ ﻊﻤ ﹰﺍﺩﻴﺠ ﹰﺎﻘﻓﺍﻭﺘ ﺕﻁﻋﺃ ﺞﺌﺎﺘﻨﻟﺍ ﻩﺫﻫ ﻙﻟﺫﻜ ﻟ
ﺎﻜﻴﻤﺎﻨﻴﺩ ﺀﺍﻭﻬﻟﺍ
) .(
CFDﺕﺎﺒﺜ ﻭ ﺔﺒﺭﺠﺘﻟﺍ ﻡﻴﻤﺼﺘ ﻲﻓ ﺯﺎﺠﻨﻻﺍ لﻼﺨ ﻥﻤ ﻙﻟﺫ ﻭ ﺓﺩﻋﺍﻭ ﺏﺭﺎﺠﺘﻟﺍ ﻩﺫﻫ ﺞﺌﺎﺘﻨ ﺕﻨﺎﻜ ﹰﺎﻤﻭﻤﻋ
ﻌﻓ
ﺙﺤﺒﻟﺍ لﺤﺍﺭﻤ لﻼﺨ ﺔﺒﺴﺘﻜﻤﻟﺍ ﺕﺍﺭﺎﻬﻤﻟﺍ ﻭ ﺕﺍﻭﺩﻻﺍ ﺔﻴﻟﺎ
.
A STUDY OF COMPRESSIBLE FLOW OVER A FLAT PLATE WITH A TEMPERATURE
STEP
MOHAMMED GHAZI ATTIAH AL-ZAHRANI
ABSTRACT
In the present study, a detailed description of an analytical solution for supersonic laminar flow over a flat plat subjected to a temperature step was done based on the present study experimental boundary conditions. All of the major physics of the resulting pressure and local heat transfer behavior, including upstream influence due to the temperature step has been presented. The results were in a good agreement with CFD simulation.
The problem of the aerodynamic heating was studied and the closed-form solutions for standard aerodynamic cases were introduced with the CFD implementation.
The experiment was conducted in KAU-AT0 wind tunnel to investigate the problem of compressible flow over a flat plate with a temperature step. A steel flat plate model was designed, manufactured, and tested. However, serious difficulties were encountered where such flat plate was put into test. These include instability of the model which destroyed the repeatability and measurement confidence. Moreover, the tunnel designed Mach number was unreachable due to vibrations generated from the model. That was evident from the PIV tests.
Considering the difficulties and time consumed with flat plate model, an axisymmetric body was designed to test the flow conditions with tunnel. Then, a final axisymmetric body model was manufactured and instrumented ready for planned tests. These experiments were conducted with similarity to the flow over a flat plate.
Tests include simultaneous experiments of the heat flux over the temperature step and the velocity vector field using the PIV technique.
Among these, heat flux measurement in short duration (e.g. 100 ms) was investigated and different techniques were studied. The Cook-Felderman technique is a common method that used for short duration heat flux measurements since it needs no initial
guess values. So, it was chosen for the heat flux data reduction method.
A state of the art PIV system was installed in the KAU-AT0 Ludwieg tube supersonic wind tunnel. The PIV system was also tested to measure the boundary layer developed over an axisymmetric body at Reynolds number of about 2×107, the results were in agreement with CFD calculations.
Due to the nature of the delicate measurements and equipments, adjustment of the experiment conditions represents a major time consuming factor which puts limitations in the planned test conditions. Therefore, it was not possible to cover a range of temperature step runs and instead testes were carried out for one temperature step of 17 K. Nevertheless, such step was sufficient to validate the outcomes of the temperature step effect regarding the local heat flux measurement. The resulting local influence in the area of the step induced large heat transfer surges that should be of concern in the design of the thermal systems. The experiment results were in a good agreement to the CFD results.
The present investigations demonstrate the high readiness of the experimental setup for carrying out accurate measurement in the available facility which can promote further studies to cover a wide range of the temperature step values at various flow and Mach number conditions.
