File:N S Laminar.svg
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![File:N S Laminar.svg](http://178.128.105.246/cars-https-upload.wikimedia.org/wikipedia/commons/thumb/a/a8/N_S_Laminar.svg/616px-N_S_Laminar.svg.png?20141106232658)
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[edit]DescriptionN S Laminar.svg |
English: SVG illustration of the Navier-Stokes Laminar problem. There is a laminar flow within a plane duct. A object obstructs the flow at the center of the duct. One may use Navier-Stokes equation by numeric method to simulate the air velocity at each point in the duct. |
Date | |
Source | Own work |
Author | IkamusumeFan |
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Source code InfoField | MATLAB code% The original author was User A1
% Retouch & Additional Comments by Ika
% Date: 11/06/2014
%Matlab script to solve a laminar flow
%in a duct problem
%Constants
inVel = 0.003; % Inlet Velocity (m/s)
fluidVisc = 1e-5; % Fluid's Viscoisity (Pa.s)
fluidDen = 1.3; %Fluid's Density (kg/m^3)
MAX_RESID = 1e-5; %uhh. residual units, yeah...
deltaTime = 1.5; %seconds?
%Kinematic Viscosity
fluidKinVisc = fluidVisc/fluidDen;
%Problem dimensions
ductLen=5; %m
ductWidth=1; %m
%grid resolution
gridPerLen = 50; % m^(-1)
gridDelta = 1/gridPerLen;
XVec = 0:gridDelta:ductLen-gridDelta;
YVec = 0:gridDelta:ductWidth-gridDelta;
%Solution grid counts
gridXSize = ductLen*gridPerLen;
gridYSize = ductWidth*gridPerLen;
%Lay grid out with Y increasing down rows
%x decreasing down cols
%so subscripting becomes (y,x) (sorry)
velX= zeros(gridYSize,gridXSize);
velY= zeros(gridYSize,gridXSize);
newVelX= zeros(gridYSize,gridXSize);
newVelY= zeros(gridYSize,gridXSize);
%Set initial condition
for i =2:gridXSize-1
for j =2:gridYSize-1
velY(j,i)=0;
velX(j,i)=inVel;
end
end
%Set boundary condition on inlet
for i=2:gridYSize-1
velX(i,1)=inVel;
end
disp(velY(2:gridYSize-1,1));
%Arbitrarily set residual to prevent
%early loop termination
resid=1+MAX_RESID;
simTime=0;
while(deltaTime)
count=0;
while(resid > MAX_RESID && count < 1e2)
count = count +1;
% the following iterations only seem plausible
for i=2:gridXSize-1
for j=2:gridYSize-1
newVelX(j,i) = velX(j,i) + deltaTime*( fluidKinVisc / (gridDelta.^2) * ...
(velX(j,i+1) + velX(j+1,i) - 4*velX(j,i) + velX(j-1,i) + ...
velX(j,i-1)) - 1/(2*gridDelta) *( velX(j,i) *(velX(j,i+1) - ...
velX(j,i-1)) + velY(j,i)*( velX(j+1,i) - velX(j,i+1))));
newVelY(j,i) = velY(j,i) + deltaTime*( fluidKinVisc / (gridDelta.^2) * ...
(velY(j,i+1) + velY(j+1,i) - 4*velY(j,i) + velY(j-1,i) + ...
velY(j,i-1)) - 1/(2*gridDelta) *( velY(j,i) *(velY(j,i+1) - ...
velY(j,i-1)) + velY(j,i)*( velY(j+1,i) - velY(j,i+1))));
end
end
%Copy the data into the front
for i=2:gridXSize - 1
for j = 2:gridYSize-1
velX(j,i) = newVelX(j,i);
velY(j,i) = newVelY(j,i);
end
end
%Set free boundary condition on inlet (dv_x/dx) = dv_y/dx = 0
for i=1:gridYSize
velX(i,gridXSize)=velX(i,gridXSize-1);
velY(i,gridXSize)=velY(i,gridXSize-1);
end
%y velocity generating vent
for i=floor(2/6*gridXSize):floor(4/6*gridXSize)
velX(floor(gridYSize/2),i) = 0;
velY(floor(gridYSize/2),i-1) = 0;
end
%calculate residual for
%conservation of mass
resid=0;
for i=2:gridXSize-1
for j=2:gridYSize-1
%mass continuity equation using central difference
%approx to differential
resid = resid + (velX(j,i+ 1)+velY(j+1,i) - ...
(velX(j,i-1) + velX(j-1,i)))^2;
% the second velY should be velX, but this is still plausible
end
end
resid = resid/(4*(gridDelta.^2))*1/(gridXSize*gridYSize);
fprintf('Time %5.3f \t log10Resid : %5.3f\n',simTime,log10(resid));
simTime = simTime + deltaTime;
end
mesh(XVec,YVec,velX)
deltaTime = input('\nnew delta time:');
end
%Plot the results
mesh(XVec,YVec,velX)
xlabel('Length (m)')
ylabel('Width (m)')
zlabel('Air Velocity (m/s, length component)')
view([110,20]) % choose a viewpoint
colorbar
% Save to file
print -depsc N_S_Laminar.eps;
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- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 23:26, 6 November 2014 | ![]() | 616 × 524 (15.42 MB) | IkamusumeFan (talk | contribs) | User created page with UploadWizard |
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